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Taylor Series for $\tan^{2}(x)$

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#taylor-expansion
413
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Finding residue of composite function.

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#complex-analysis #taylor-expansion #residue-calculus #laurent-series
115
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calculation of limit of $\lim_{\theta\to0}\frac{\cos\left(\frac\pi2\cos\theta\right)}{\sin\theta}$

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#limits #taylor-expansion
443
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Understanding the Maclaurin Series

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#integration #taylor-expansion
1.1k
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Extract coefficients of series of polynomials

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#sequences-and-series #power-series #taylor-expansion
104
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Function approximations in higher dimensions

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#multivariable-calculus #taylor-expansion
210
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I have found a Taylor series and a Maclaurin series for a function about x=0.... I have a couple of questions.

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#sequences-and-series #convergence-divergence #summation #power-series #taylor-expansion
334
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Taylor series approximations of angular acceleration for a pendulum when the angle is small

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#calculus #taylor-expansion
766
Views

Prove $\frac{d}{dx}(e^x)=e^x$ with Taylor series and power rule

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#calculus #derivatives #taylor-expansion
763
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Using termwise (term-by-term) differentiation on an infinite series to satisfy a differential equation.

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#sequences-and-series #ordinary-differential-equations #derivatives #power-series #taylor-expansion
72
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Finding the sum $\sum_{n=0}^\infty\frac{(x+1)^{n+2}}{(n+2)!}$. I cannot use my usual methods that I am use to.

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#sequences-and-series #summation #power-series #taylor-expansion
1.1k
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Finding the first 3 terms of a power series... I am confused as to whether I can just plug numbers in or if there is more.

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#sequences-and-series #functional-analysis #summation #power-series #taylor-expansion
379
Views

Series expansion of $xy'=y$

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#ordinary-differential-equations #power-series #taylor-expansion
515
Views

Calculating the approximation of an integral using the first four terms of a Maclaurin series.

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#integration #sequences-and-series #summation #taylor-expansion #exponential-function
45
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Is there a general pattern for all integrals of the form $\sin^{k/2}x$ where $k$ is an integer?

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#calculus #integration #power-series #taylor-expansion #indefinite-integrals

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