List questions from limits

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Question regarding limits of multivariable functions - is it really zero?

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Computing the limit of $\lambda y_1 - \log( \sum_{i=1}^N a_i e^{\lambda y_i})$ as $\lambda$ goes to negative infinity

Published on 13 Apr 2026 - 11:05

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General limit of multivariable rational functions

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Limit involving $x$ raised to $\sin (1/x)$

Published on 15 Apr 2026 - 0:09

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Prob. 12, Sec. 4.2, in Bartle & Sherbert's INTRO TO REAL ANALYSIS: If $f(x+y)=f(x)+f(y)$ for all $x, y$ and if $\lim_{x\to 0} f(x)$ exists, . . .

Published on 16 Apr 2026 - 2:27

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Prob. 15, Sec. 4.2, in Bartle & Sherbert's INTRO TO REAL ANALYSIS: $\lim_{x\to c}\sqrt{f(x)}=\sqrt{\lim_{x\to c}f(x)}$

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How's g(x) = sin(x)/x removal discontinuity?

Published on 12 Apr 2026 - 19:55

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Taking Cauchy’s Formulas to the Limit

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Contour Integral of Geometric Series

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Horizontal Asymptote of a Function with no X values

Published on 06 May 2026 - 7:34

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$\lim_{x\to 0} x^{\alpha}e^{|\log x|^{1/2}}=0$

Published on 17 Apr 2026 - 1:06

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Integrals: can we take limits ‘partially’?

Published on 13 Apr 2026 - 15:54

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Proving a Polynomial Limit where x → 0

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405

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Asymptotic behaviour of the solution of a PDE

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Limit of a quotient of factorials

Question regarding limits of multivariable functions - is it really zero?

Computing the limit of $\lambda y_1 - \log( \sum_{i=1}^N a_i e^{\lambda y_i})$ as $\lambda$ goes to negative infinity

General limit of multivariable rational functions

Limit involving $x$ raised to $\sin (1/x)$

Prob. 12, Sec. 4.2, in Bartle & Sherbert's INTRO TO REAL ANALYSIS: If $f(x+y)=f(x)+f(y)$ for all $x, y$ and if $\lim_{x\to 0} f(x)$ exists, . . .

Prob. 15, Sec. 4.2, in Bartle & Sherbert's INTRO TO REAL ANALYSIS: $\lim_{x\to c}\sqrt{f(x)}=\sqrt{\lim_{x\to c}f(x)}$

How's g(x) = sin(x)/x removal discontinuity?

Taking Cauchy’s Formulas to the Limit

Contour Integral of Geometric Series

Horizontal Asymptote of a Function with no X values

$\lim_{x\to 0} x^{\alpha}e^{|\log x|^{1/2}}=0$

Integrals: can we take limits ‘partially’?

Proving a Polynomial Limit where x → 0

Asymptotic behaviour of the solution of a PDE

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