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Recent questions tagged limits

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GATE Civil 2021 Set 2 | Question: 1
The value of $\lim \limits_{x\rightarrow \infty } \dfrac{x \:\text{ln}\left ( x \right )}{1+x^{2}}$ is $0$ $1.0$ $0.5$ $\infty$
The value of $\lim \limits_{x\rightarrow \infty } \dfrac{x \:\text{ln}\left ( x \right )}{1+x^{2}}$ is$0$$1.0$$0.5$$\infty$
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GATE Civil 2021 Set 1 | Question: 18
Consider the limit: $\lim_{x\rightarrow 1}\left ( \frac{1}{\text{ln}\:x} - \frac{1}{x-1}\right )$ The limit (correct up to one decimal place) is _____________
Consider the limit:$$\lim_{x\rightarrow 1}\left ( \frac{1}{\text{ln}\:x} - \frac{1}{x-1}\right )$$The limit (correct up to one decimal place) is _____________
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GATE2020-CE-1-2
The value of $\displaystyle{} \lim_{x\to\infty}\dfrac{x^2-5x+4}{4x^2+2x}$ is $0 \\$ $\dfrac{1}{4} \\$ $\dfrac{1}{2} \\$ $1$
The value of $\displaystyle{} \lim_{x\to\infty}\dfrac{x^2-5x+4}{4x^2+2x}$ is$0 \\$$\dfrac{1}{4} \\$$\dfrac{1}{2} \\$$1$
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GATE2020 CE-2-2
The value of $\lim_{x\to\infty}\dfrac{\sqrt{9x^2+2020}}{x+7}\:\text{is}$ $\dfrac{7}{9}$ $1$ $3$ indeterminable
The value of $$\lim_{x\to\infty}\dfrac{\sqrt{9x^2+2020}}{x+7}\:\text{is}$$$\dfrac{7}{9}$$1$$3$indeterminable
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GATE2019 CE-1: 1
Which one of the following is correct? $\displaystyle{} \lim_{x\rightarrow 0} \left( \dfrac{\sin4x}{\sin2x}\right)=2\;\text{and}\: \lim_{x\rightarrow 0} \left( \dfrac{\tan x}{x}\right)=1$ ...
Which one of the following is correct?$\displaystyle{} \lim_{x\rightarrow 0} \left( \dfrac{\sin4x}{\sin2x}\right)=2\;\text{and}\: \lim_{x\rightarrow 0} \left( \dfrac{\tan...
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GATE2019 CE-2: 3
The following inequality is true for all $x$ close to $0$. $2-\dfrac{x^2}{3} < \dfrac{x \sin x}{1- \cos x} <2$ What is the value of $\underset{x \to 0}{\lim} \dfrac{x \sin x}{1 – \cos x}$? $0$ $1/2$ $1$ $2$
The following inequality is true for all $x$ close to $0$.$$2-\dfrac{x^2}{3} < \dfrac{x \sin x}{1- \cos x} <2$$What is the value of $\underset{x \to 0}{\lim} \dfrac{x \si...
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GATE2016-2-5
What is the value of $\underset{x \rightarrow 0 \\ y \rightarrow 0}{\lim} \dfrac{xy}{x^2+y^2}$? $1$ $-1$ $0$ Limit does not exist
What is the value of $\underset{x \rightarrow 0 \\ y \rightarrow 0}{\lim} \dfrac{xy}{x^2+y^2}$?$1$$-1$$0$Limit does not exist
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GATE2017 CE-1: 21
$\underset{x \to 0}{\lim} \bigg( \dfrac{\tan x}{x^2-x} \bigg)$ is equal to _________
$\underset{x \to 0}{\lim} \bigg( \dfrac{\tan x}{x^2-x} \bigg)$ is equal to _________
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GATE2015-2-4
$\underset{x \to \infty}{\lim} \bigg( 1+ \dfrac{1}{x} \bigg)^{2x} $ is equal to $e^{-2}$ $e$ $1$ $e^2$
$\underset{x \to \infty}{\lim} \bigg( 1+ \dfrac{1}{x} \bigg)^{2x} $ is equal to$e^{-2}$$e$$1$$e^2$
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GATE2014-2-26
The expression $\displaystyle{} \lim_{a \to 0} \dfrac{x^a-1}{a}$ is equal to $\log x$ $0$ $x \log x$ $\infty$
The expression $\displaystyle{} \lim_{a \to 0} \dfrac{x^a-1}{a}$ is equal to$\log x$$0$$x \log x$$\infty$
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GATE2014-1-1
$\underset{x \to \infty}{\lim} \bigg( \dfrac{x+\sin x}{x} \bigg)$ equals to $- \infty$ $0$ $1$ $\infty$
$\underset{x \to \infty}{\lim} \bigg( \dfrac{x+\sin x}{x} \bigg)$ equals to$- \infty$$0$$1$$\infty$
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