messages listlengths 3 3 | topic stringclasses 1
value | subtopic stringclasses 14
values |
|---|---|---|
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\sin (2 x)+1$"
},
{
"role": "assistant",
"content": "$\\frac{1}{2} \\sec... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$-\\tan ^{-1}(2 x)$"
},
{
"role": "assistant",
"content": "$-\\frac{x}{2}$... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\log \\left(\\frac{4 x}{5}\\right)$"
},
{
"role": "assistant",
"content... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$32 x^5$"
},
{
"role": "assistant",
"content": "$\\frac{(x+32)^2}{12800}+... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the third order series of the inverse of the following function around 3:\n$\\sin ^{-1}(3 x)$"
},
{
"role": "assistant",
"content": "$\\frac{x}{3}-\\... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\tan (x)$"
},
{
"role": "assistant",
"content": "$\\frac{\\tan (4) (x+\... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the fifth order series of the inverse of the following function around 5:\n$\\sin ^2(4 x)$"
},
{
"role": "assistant",
"content": "$\\frac{x^{3/2}}{24... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$e^{4 x}$"
},
{
"role": "assistant",
"content": "$-\\frac{\\left(x-e^8\\r... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the third order series of the inverse of the following function around 3:\n$256 x^4$"
},
{
"role": "assistant",
"content": "$-\\frac{7 (x-20736)^3}{3... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$-\\frac{\\sqrt[3]{x} \\cot (5 x)}{\\sqrt[3]{2}}$"
},
{
"role": "assistant",
... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$-\\sin (x)$"
},
{
"role": "assistant",
"content": "$-\\sec (2) (x-\\sin (... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$e^{-x}$"
},
{
"role": "assistant",
"content": "$\\frac{\\left(x-e^5\\rig... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$2^{2/3} \\sqrt[3]{x^5}$"
},
{
"role": "assistant",
"content": "$\\frac{\... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the third order series of the inverse of the following function around 3:\n$\\cos (x)$"
},
{
"role": "assistant",
"content": "$-i \\sqrt{2} \\sqrt{x-... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\sqrt[3]{2} \\sqrt[3]{x}$"
},
{
"role": "assistant",
"content": "$\\fra... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$e^{2 x}$"
},
{
"role": "assistant",
"content": "$\\frac{x-1}{2}-\\frac{1... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$-\\tan (2 x)$"
},
{
"role": "assistant",
"content": "$\\frac{x+\\tan (6)}... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$x^2$"
},
{
"role": "assistant",
"content": "$-\\frac{1}{64} (x-4)^2+\\fr... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\tan ^{-1}(3 x)$"
},
{
"role": "assistant",
"content": "$-10 \\left(x-... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\sin (4 x)$"
},
{
"role": "assistant",
"content": "$-\\frac{x}{4}$"
... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\frac{1}{x^{10}}$"
},
{
"role": "assistant",
"content": "$\\frac{1}{\\sq... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\sin \\left(\\frac{4 x}{3}\\right)$"
},
{
"role": "assistant",
"content"... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$e^{-5 x}$"
},
{
"role": "assistant",
"content": "$\\frac{1}{10} e^{30} \... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the fourth order series of the inverse of the following function around 4:\n$\\sqrt{3} \\sqrt{x}$"
},
{
"role": "assistant",
"content": "$\\frac{1}{3... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\sqrt[3]{x}$"
},
{
"role": "assistant",
"content": "$3 (x-1)^2+3 (x-1)+... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the third order series of the inverse of the following function around 3:\n$\\frac{1}{256 x^4}$"
},
{
"role": "assistant",
"content": "$1966080 \\lef... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$e^{2 x}$"
},
{
"role": "assistant",
"content": "$\\frac{x-e^4}{2 e^4}+2$"... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the third order series of the inverse of the following function around 3:\n$-\\frac{1}{3125 x^5}$"
},
{
"role": "assistant",
"content": "$2685546875 ... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$-\\sqrt[3]{\\frac{23}{5}} \\sqrt[3]{x}$"
},
{
"role": "assistant",
"conte... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the third order series of the inverse of the following function around 3:\n$e^{-2 x}$"
},
{
"role": "assistant",
"content": "$-\\frac{\\left(x-e^2\\r... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the fifth order series of the inverse of the following function around 5:\n$-\\tan (3 x)-\\sinh ^{-1}(2 x)$"
},
{
"role": "assistant",
"content": "$-... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the third order series of the inverse of the following function around 3:\n$e^{-3 x}$"
},
{
"role": "assistant",
"content": "$-\\frac{\\left(x-e^9\\r... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the third order series of the inverse of the following function around 3:\n$x^2$"
},
{
"role": "assistant",
"content": "$\\frac{1}{16} (x-1)^3-\\frac... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\cot (4 x) \\sinh ^{-1}(2 x)$"
},
{
"role": "assistant",
"content": "$\\... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the third order series of the inverse of the following function around 3:\n$\\frac{81 x^2}{4}-\\sin \\left(\\frac{5 x}{2}\\right)$"
},
{
"role": "assista... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\tan (x)$"
},
{
"role": "assistant",
"content": "$\\frac{\\tan (1) (x+\... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$e^{-2 x}$"
},
{
"role": "assistant",
"content": "$\\frac{1}{4} e^4 \\lef... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\tan ^{-1}(2 x)$"
},
{
"role": "assistant",
"content": "$505 \\left(x-\... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\sin (x)$"
},
{
"role": "assistant",
"content": "$\\sec (5) (x-\\sin (5... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$-\\tan (3 x)$"
},
{
"role": "assistant",
"content": "$\\frac{x-\\tan (3)}... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$-\\cos (x) \\csc (2 x)$"
},
{
"role": "assistant",
"content": "$\\frac{x-... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\frac{1}{16 x^4}$"
},
{
"role": "assistant",
"content": "$-10485760 \\l... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\sqrt[3]{2} \\sqrt[3]{x^3}$"
},
{
"role": "assistant",
"content": "$5-... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$2^{2/3} \\sqrt[3]{x}$"
},
{
"role": "assistant",
"content": "$-\\frac{3 ... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$e^{-4 x}$"
},
{
"role": "assistant",
"content": "$\\frac{1}{8} (x-1)^2+\... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\tan ^{-1}(5 x)$"
},
{
"role": "assistant",
"content": "$202 \\left(x-\... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$2 \\sqrt{x}$"
},
{
"role": "assistant",
"content": "$\\frac{1}{4} \\left... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\frac{1}{x^4}$"
},
{
"role": "assistant",
"content": "$256 \\left(x-\\fr... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$-\\tan \\left(\\frac{3 x}{2}\\right)$"
},
{
"role": "assistant",
"content... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$e^{-4 x}$"
},
{
"role": "assistant",
"content": "$\\frac{\\left(x-e^{20}... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the third order series of the inverse of the following function around 3:\n$e^{3 x}$"
},
{
"role": "assistant",
"content": "$\\frac{\\left(x-e^{12}\\... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$e^{-\\frac{7 x^4}{2}}$"
},
{
"role": "assistant",
"content": "$\\frac{22... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\cos (5 x)-\\sin (5 x)$"
},
{
"role": "assistant",
"content": "$\\frac{x... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\sqrt{2} \\sqrt{-x}$"
},
{
"role": "assistant",
"content": "$-\\frac{1}... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the third order series of the inverse of the following function around 3:\n$\\sin (x)$"
},
{
"role": "assistant",
"content": "$\\frac{x^3}{6}+x$"
}... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\tan (2 x)$"
},
{
"role": "assistant",
"content": "$-\\frac{2 \\tan (4)... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\frac{1}{x^5}$"
},
{
"role": "assistant",
"content": "$-\\frac{3}{25} (... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the sixth order series of the inverse of the following function around 6:\n$\\sqrt{\\frac{7}{2}} \\sqrt{x^2}$"
},
{
"role": "assistant",
"content": "... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\tan ^{-1}(x)$"
},
{
"role": "assistant",
"content": "$10 \\left(x-\\ta... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\sqrt{5} \\sqrt{x}-e^{2 x}$"
},
{
"role": "assistant",
"content": "$\\f... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\tan ^{-1}(x)$"
},
{
"role": "assistant",
"content": "$30 \\left(x+\\t... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the third order series of the inverse of the following function around 3:\n$-\\frac{1}{3 x}$"
},
{
"role": "assistant",
"content": "$432 \\left(x+\\f... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\tan (2 x)$"
},
{
"role": "assistant",
"content": "$\\frac{x+\\tan (10)}... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$e^{2 x}$"
},
{
"role": "assistant",
"content": "$\\frac{x-e^4}{2 e^4}+2$"... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the third order series of the inverse of the following function around 3:\n$\\sqrt{\\frac{5}{2}} \\sqrt{-x}$"
},
{
"role": "assistant",
"content": "$... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the fifth order series of the inverse of the following function around 5:\n$\\tan (x)$"
},
{
"role": "assistant",
"content": "$\\frac{x^5}{5}-\\frac{... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\sqrt{2} \\sqrt{x}$"
},
{
"role": "assistant",
"content": "$\\sqrt{10} \... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\log (2 x)$"
},
{
"role": "assistant",
"content": "$(x-2 \\log (2))^2+2... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$-\\tan (x)$"
},
{
"role": "assistant",
"content": "$\\frac{x-\\tan (1)}{-... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\tan ^{-1}(5 x)$"
},
{
"role": "assistant",
"content": "$-202 \\left(x... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the third order series of the inverse of the following function around 3:\n$e^{2 x}$"
},
{
"role": "assistant",
"content": "$\\frac{\\left(x-e^2\\rig... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\sin (4 x)$"
},
{
"role": "assistant",
"content": "$-\\frac{1}{4} \\se... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\tan ^{-1}(2 x)$"
},
{
"role": "assistant",
"content": "$111 \\left(x-\... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\tan (3 x)$"
},
{
"role": "assistant",
"content": "$-\\frac{3 \\tan (6... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$e^x$"
},
{
"role": "assistant",
"content": "$-\\frac{\\left(x-e^4\\right... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the sixth order series of the inverse of the following function around 6:\n$-\\tanh (3 x)$"
},
{
"role": "assistant",
"content": "$-\\frac{x^5}{15}-\... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\sqrt{-x}$"
},
{
"role": "assistant",
"content": "$-\\left(x-\\sqrt{3}\... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$e^{-2 x}$"
},
{
"role": "assistant",
"content": "$\\frac{1}{4} e^{12} \\... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the third order series of the inverse of the following function around 3:\n$-\\frac{1}{x}$"
},
{
"role": "assistant",
"content": "$16 \\left(x-\\frac... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the third order series of the inverse of the following function around 3:\n$-\\frac{8}{27 x^3}$"
},
{
"role": "assistant",
"content": "$6967296 \\lef... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\sqrt[3]{\\frac{17}{5}} \\sqrt[3]{x}$"
},
{
"role": "assistant",
"cont... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\tan (x)$"
},
{
"role": "assistant",
"content": "$-\\frac{\\tan (4) (x... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\tan (x)$"
},
{
"role": "assistant",
"content": "$\\frac{\\tan (3) (x-... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$e^x$"
},
{
"role": "assistant",
"content": "$\\frac{x-e}{e}+1$"
}
] | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$2 \\sqrt{x}$"
},
{
"role": "assistant",
"content": "$\\frac{1}{4} (x-2)^... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$e^{4 x^4}$"
},
{
"role": "assistant",
"content": "$\\frac{19 \\left(x-e^... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-1024 x^5$"
},
{
"role": "assistant",
"content": "$\\frac{(x-1024)^2}{13... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$e^{4 x}$"
},
{
"role": "assistant",
"content": "$-\\frac{\\left(x-e^4\\r... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$e^x$"
},
{
"role": "assistant",
"content": "$-\\frac{1}{2} e^2 \\left(x-... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\sqrt[3]{2} \\sqrt[3]{x}$"
},
{
"role": "assistant",
"content": "$-\\f... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the fifth order series of the inverse of the following function around 5:\n$\\sqrt{5} \\sqrt{-x}$"
},
{
"role": "assistant",
"content": "$-\\frac{1}{... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\sqrt[3]{x}-\\tan ^{-1}(x)$"
},
{
"role": "assistant",
"content": "$-6 \... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-27 x^3$"
},
{
"role": "assistant",
"content": "$-\\frac{(x+27)^2}{6561}... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\sqrt{3} \\sqrt{x}$"
},
{
"role": "assistant",
"content": "$\\frac{1}{3... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\tan ^{-1}(5 x)$"
},
{
"role": "assistant",
"content": "$\\frac{101}{5} ... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\frac{3 x}{5}+e^{-17 x/5}$"
},
{
"role": "assistant",
"content": "$\\fr... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$e^{3 x}$"
},
{
"role": "assistant",
"content": "$\\frac{x-e^3}{3 e^3}+1$"... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\log (3 x)$"
},
{
"role": "assistant",
"content": "$x+1-\\log (3)$"
}
... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the sixth order series of the inverse of the following function around 6:\n$4 x$"
},
{
"role": "assistant",
"content": "$\\frac{x-16}{4}+4$"
}
] | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\cos (3 x)$"
},
{
"role": "assistant",
"content": "$\\frac{1}{3} \\csc (... | calculus | series_inverse |
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