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14 votes
7 answers
1
GATE CSE 2019 | Question: 13
Compute $\displaystyle \lim_{x \rightarrow 3} \frac{x^4-81}{2x^2-5x-3}$ $1$ $53/12$ $108/7$ Limit does not exist
Compute $\displaystyle \lim_{x \rightarrow 3} \frac{x^4-81}{2x^2-5x-3}$$1$$53/12$$108/7$Limit does not exist
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1 votes
2 answers
2
GATE DS&AI 2024 | Question: 50
Evaluate the following limit: \[ \lim _{x \rightarrow 0} \frac{\ln \left(\left(x^{2}+1\right) \cos x\right)}{x^{2}}= \]
Evaluate the following limit:\[\lim _{x \rightarrow 0} \frac{\ln \left(\left(x^{2}+1\right) \cos x\right)}{x^{2}}= \]
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26 votes
6 answers
4
GATE CSE 2015 Set 1 | Question: 4
$\displaystyle \lim_{x\rightarrow \infty } x^{ \tfrac{1}{x}}$ is $\infty $ $0$ $1$ Not defined
$\displaystyle \lim_{x\rightarrow \infty } x^{ \tfrac{1}{x}}$ is$\infty $$0$$1$Not defined
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25 votes
9 answers
6
GATE CSE 2008 | Question: 1
$\displaystyle \lim_{x \to \infty}\frac{x-\sin x}{x+\cos x}$ equals $1$ $-1$ $\infty$ $-\infty$
$\displaystyle \lim_{x \to \infty}\frac{x-\sin x}{x+\cos x}$ equals$1$$-1$$\infty$$-\infty$
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0 votes
1 answer
7
Limit
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1 votes
1 answer
8
GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 5
$\lim _{x \rightarrow 2} \frac{\sqrt{x}-\sqrt{2}}{x-2}$ $0$ $\sqrt{2}$ $\frac{1}{2 \sqrt{2}}$ $\frac{1}{\sqrt{2}}$
$\lim _{x \rightarrow 2} \frac{\sqrt{x}-\sqrt{2}}{x-2}$$0$$\sqrt{2}$$\frac{1}{2 \sqrt{2}}$$\frac{1}{\sqrt{2}}$
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12 votes
4 answers
9
GATE CSE 2022 | Question: 24
The value of the following limit is ________________. $\lim_{x \rightarrow 0^{+}} \frac{\sqrt{x}}{1-e^{2\sqrt{x}}}$
The value of the following limit is ________________.$$\lim_{x \rightarrow 0^{+}} \frac{\sqrt{x}}{1-e^{2\sqrt{x}}}$$
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31 votes
8 answers
10
GATE CSE 2010 | Question: 5
What is the value of $ \displaystyle\lim_{n \to \infty}\left(1 - \frac{1}{n}\right)^{2n}$ ? $0$ $e^{-2}$ $e^{-1/2}$ $1$
What is the value of $ \displaystyle\lim_{n \to \infty}\left(1 - \frac{1}{n}\right)^{2n}$ ?$0$$e^{-2}$$e^{-1/2}$$1$
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0 votes
1 answer
11
calculus
How do we solve this question: $\lim n \to \infty \sqrt{n^2 + n} - {\sqrt{n^2 +1}}$
How do we solve this question: $\lim n \to \infty \sqrt{n^2 + n} - {\sqrt{n^2 +1}}$
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0 votes
1 answer
12
LIMIT AND CONTINUITY
1.Evaluate the following definite integral $\int^{130}_{130}\frac{x^{3}-x\sin(x)+\cos(x)}{x^{^{2}}+1}dx$
1.Evaluate the following definite integral $\int^{130}_{130}\frac{x^{3}-x\sin(x)+\cos(x)}{x^{^{2}}+1}dx$
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0 votes
0 answers
13
LIMIT AND CONTINUITY
Determine the volume of the solid obtained by rotating the portion of the region bounded by $y=\sqrt[3]{x}$ and $y=\frac{x}{4}$ that lies in the first quadrant about the y-axis.
Determine the volume of the solid obtained by rotating the portion of the region bounded by $y=\sqrt[3]{x}$ and $y=\frac{x}{4}$ that lies in the first quadrant about the ...
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0 votes
0 answers
14
LIMIT AND CONTINUITY integration
Depramine the area of region bounded by $y=2x^{2}+10$ and $y=4x+16$
Depramine the area of region bounded by $y=2x^{2}+10$ and $y=4x+16$
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0 votes
0 answers
15
LIMIT AND CONTINUITY
Differentiate each of the following. $g(x)=\int ^{x}_{-4}e^{2t}cos^{2}(1-5t)dt$
Differentiate each of the following. $g(x)=\int ^{x}_{-4}e^{2t}cos^{2}(1-5t)dt$
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0 votes
1 answer
16
Applied Mathematics-IB
Use the Squeeze Theorem to determine the value of $\lim_{x\rightarrow 0} x^{4}\sin (\frac{\pi}{x}).$x^{4}\sin (\frac{\pi}{x}).$
Use the Squeeze Theorem to determine the value of $\lim_{x\rightarrow 0} x^{4}\sin (\frac{\pi}{x}).$$x^{4}\sin (\frac{\pi}{x}).$
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0 votes
1 answer
17
Applied Mathematics-IB
Given that $7x\leq f\left ( x \right )\leq 3x^{2}+2$ for all determine the value of $\lim x\rightarrow 0 f(x)$
Given that $7x\leq f\left ( x \right )\leq 3x^{2}+2$ for all determine the value of $\lim x\rightarrow 0 f(x)$
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0 votes
0 answers
18
Applied Mathematics-IB
Determine all the number(s) c which satisfy the conclusion of Roles' Theorem for the given function and interval $f(x)=x^{2}-2x-8 $ on $ [-1,3]$
Determine all the number(s) c which satisfy the conclusion of Roles' Theorem for the given function and interval $f(x)=x^{2}-2x-8 $ on $ [-1,3]$
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0 votes
0 answers
19
Applied Mathematics-IB
sketch the graph of $h(x)=-(x+4)^{3}$ and identify all the relative extrema and absolute extrema of the function.
sketch the graph of $h(x)=-(x+4)^{3}$ and identify all the relative extrema and absolute extrema of the function.
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3 votes
1 answer
20
#Made Easy
Find the value of $\lim_{x \rightarrow 0 } \dfrac{x \tan2x - 2x\tan x}{(1-\cos 2x)^2} \rule{1 in}{.5 pt}.$
Find the value of $\lim_{x \rightarrow 0 } \dfrac{x \tan2x - 2x\tan x}{(1-\cos 2x)^2} \rule{1 in}{.5 pt}.$
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