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Expectation and Variance of Y = g(Z)

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#statistics #random-variables #taylor-expansion #expectation #variance
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Taylor polynomial remainder

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#calculus #taylor-expansion
129
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Series expansion of $\left(1 + x^2\right)^{-1/2}$

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#sequences-and-series #convergence-divergence #power-series #taylor-expansion
395
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Prove upper bound on derivative

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#real-analysis #derivatives #taylor-expansion
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Taylor Series of $e^{-1/x^2}$ about $0$

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#taylor-expansion
3.2k
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Determining if a function described by a Taylor series has a relative extremum at a point

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#calculus #derivatives #taylor-expansion
1k
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Approximation of functions for small or large values of $x$ through $o(x)$ or $O(x)$.

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#real-analysis #taylor-expansion
97
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Approximating the hessian using gradient

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#real-analysis #optimization #taylor-expansion #approximation #hessian-matrix
941
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How to evaluate $\lim_{x \rightarrow \infty} \left(\left(\frac{x+1}{x-1}\right)^x -e^2\right){x}^2$

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#real-analysis #limits #taylor-expansion #exponential-function
91
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Can a Taylor polynomial of a function around a certain value yield different polynomials?

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#calculus #taylor-expansion
388
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Compute Maclaurin expansion of $f(x)=e^{5x^2}$ and find a type for $f^{(n)}(0)$

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#power-series #taylor-expansion #exponential-function
2.8k
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How to prove $\ln(x)$ is analytic everywhere?

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#calculus #logarithms #taylor-expansion #proof-explanation #analyticity
51
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Question on notation of 3rd degree Taylor expansion

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#calculus #multivariable-calculus #taylor-expansion #integral-equations
737
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Find a Maclaurin series for a sum of two functions

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#calculus #taylor-expansion
251
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Root of a polynomial $p(x)$ and asymptotic behaviour of the Taylor series of $\frac{1}{p(x)}$

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#polynomials #taylor-expansion #roots

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