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Why limit of $\lim_{x \to 0}(x-\ln(x+1)+\cos(xe^{-x}))^{\frac{9\cot^{3}(x)}{2}}$ is $e^3$?

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#limits #taylor-expansion
180
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Taylor series expansion rearrangement

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#calculus #sequences-and-series #taylor-expansion #absolute-convergence
122
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Graphical intuition behind general Taylor formula

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#taylor-expansion #frechet-derivative
31
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Taylor series coefficient calculation

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#sequences-and-series #complex-analysis #power-series #taylor-expansion
178
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when does $1-x-\frac{x^2}{2!}+\frac{x^3}{3!}-...$converge

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#calculus #convergence-divergence #taylor-expansion
269
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Can you write $1-x-\frac{x^2}{2!}+\frac{x^3}{3!}-\dots$ with elementary functions

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#calculus #taylor-expansion #elementary-functions
602
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Prove integral inequality: $\int_{0}^{\frac{\pi}{2}}e^{\sin x}\,dx\geq\frac{\pi}{2}(e-1)$

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#calculus #inequality #definite-integrals #taylor-expansion
239
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Find $\lim_{x\to 0^{+}} \frac{\theta(x)}{x}$

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#real-analysis #calculus #limits #definite-integrals #taylor-expansion
63
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Derivation of Taylor polynomial

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#calculus #taylor-expansion
177
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find explicit expression for the function $f(x)= \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)(x+1)^{2n}}$

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#calculus #sequences-and-series #power-series #taylor-expansion
239
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A surprisingly simple determinant

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#taylor-expansion #determinant #fourier-series
163
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Function (Taylor series) of Jordan canonical form about arbitrary point

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#linear-algebra #matrices #power-series #taylor-expansion #jordan-normal-form
445
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Multivariate Taylor series with Hessian evaluated at a linear combination of $x$ and $\Delta x$

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#multivariable-calculus #taylor-expansion
920
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What is the residue of $z^2 \cos(\frac{1}{z})$

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#complex-analysis #taylor-expansion #laurent-series
52
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Show that the error is less than $C_0a^4/4$

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#calculus #integration #polynomials #taylor-expansion #approximation

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