List questions from limits

Published on 14 Apr 2026 - 12:30

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Limit $\lim _ { x \to - \infty } \frac{ x }{(\sqrt{ x ^2} + \sqrt{ x ^4 + 1} ) + \sqrt{ 2} ) ( \sqrt{ x ^4 + 1} + x ^2) }$

Published on 17 Apr 2026 - 9:34

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Finding a limit of recursively given sequence

Published on 30 Apr 2026 - 8:01

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Calculate $\int_{-\infty}^{\infty} \frac{\sin(mx)}{x(a^2+x^2)} dx$

Published on 16 Apr 2026 - 2:40

353

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How to prove that for $- x\log{(x)}\le\sqrt{x}$

Published on 14 Apr 2026 - 2:06

790

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Finding upper bound of a linear function

Published on 11 Apr 2026 - 13:32

41

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Showing $\lim_{x \to -3}|\frac{5-x}{3+x}| = +\infty$ using the definition of the limit

Published on 16 Apr 2026 - 3:16

124

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What is the limit of $\frac{n^k}{a^n}$

Published on 16 Apr 2026 - 12:24

108

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How to prove that $- x\ln{(x)}\le\sqrt{x}$ for $0<x<1$

Published on 15 Apr 2026 - 2:06

300

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Prove that, $\lim_{n \to \infty} n^{1 \over \sqrt n}= 1$

Published on 16 Apr 2026 - 14:34

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why isn't this characteristic $1$ when n $\to \infty$

Published on 25 Mar 2026 - 17:32

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Prove that f(x) vanishes in whole of its domain.

Published on 13 Apr 2026 - 11:49

445

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Evaluating $\lim_{n\rightarrow\infty} \int_{0}^{\pi} \frac {\sin x}{1+ \cos^2 (nx)} dx$

Published on 16 Apr 2026 - 14:14

109

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$\lim_{x\to +\infty} \sin \left[2\pi \sqrt{ \lfloor x\rfloor^{2}+\lfloor \frac{x}{3}\rfloor} \right] $

Published on 17 Apr 2026 - 7:30

336

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For what values of $\alpha$, does this integral converge?

Published on 14 Apr 2026 - 12:22

List Question

limit of $\lim_{x\to\infty} \frac{f(x)}{f'(x)} $

Limit $\lim _ { x \to - \infty } \frac{ x }{(\sqrt{ x ^2} + \sqrt{ x ^4 + 1} ) + \sqrt{ 2} ) ( \sqrt{ x ^4 + 1} + x ^2) }$

Finding a limit of recursively given sequence

Calculate $\int_{-\infty}^{\infty} \frac{\sin(mx)}{x(a^2+x^2)} dx$

How to prove that for $- x\log{(x)}\le\sqrt{x}$

Finding upper bound of a linear function

Showing $\lim_{x \to -3}|\frac{5-x}{3+x}| = +\infty$ using the definition of the limit

What is the limit of $\frac{n^k}{a^n}$

How to prove that $- x\ln{(x)}\le\sqrt{x}$ for $0<x<1$

Prove that, $\lim_{n \to \infty} n^{1 \over \sqrt n}= 1$

why isn't this characteristic $1$ when n $\to \infty$

Prove that f(x) vanishes in whole of its domain.

Evaluating $\lim_{n\rightarrow\infty} \int_{0}^{\pi} \frac {\sin x}{1+ \cos^2 (nx)} dx$

$\lim_{x\to +\infty} \sin \left[2\pi \sqrt{ \lfloor x\rfloor^{2}+\lfloor \frac{x}{3}\rfloor} \right] $

For what values of $\alpha$, does this integral converge?

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