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is this correct? $\lim\limits_{x\to a}f(x)^{g(x)} = [\lim\limits_{x\to a}f(x)]^{\lim\limits_{x\to a}g(x)}$

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#limits
48
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Undefined limit

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#real-analysis #analysis #limits #continuity
50
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If a complicated function $F$ satisfies $F(x,y)=R(x,y)$, where $R$ is a rational function, can we safely take limits on both sides?

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#real-analysis #limits #multivariable-calculus #functional-equations #rational-functions
51
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$\lim_{t \to 0} \dfrac{f(g(1 + t, 2), h(1 + t, 2)) - f(g(1, 2), h(1, 2)) }{t} ?$

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#limits #partial-derivative
93
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Can $\{n!\log n\}$ converge to $1$?

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#real-analysis #number-theory #limits #factorial #fractional-part
56
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Stirling approximation of logarithms

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#sequences-and-series #limits
159
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How to compute $\prod_{1\le i\le n} \left(1-\frac{1}{2^i}\right)$

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#calculus #sequences-and-series #combinatorics #number-theory #limits
241
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Calculating $\lim \limits_{n \to \infty} \int_ {-\infty}^\infty e^{-x^2}\cos(nx)\, dx$

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#calculus #limits #improper-integrals #fourier-series #fourier-transform
1.4k
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Show that $\lim_{n \to \infty} \int_0^{\infty} \frac{1}{1+x^n}~dx = 1$

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#calculus #integration #limits #convergence-divergence #definite-integrals
189
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Need help with this limit problem from Stewart's Calculus

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#calculus #limits
126
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Ball-dimension of space

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#limits #reference-request #metric-spaces #dynamical-systems
52
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Proving limit involving random variables

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#probability #limits #random-variables
76
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Finding the limit of a series.

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#sequences-and-series #limits
81
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Two variable-limit.

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#limits
79
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Making a limit substitution rigorous

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#calculus #limits #multivariable-calculus

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