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Syllabus: Limits, Continuity, and Differentiability, Maxima and minima, Mean value theorem, Integration.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2024-1} &\textbf{2024-2} &\textbf{2023} &\textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} &1&1&2& 1 &1&1&1&1.16&2
\\\hline\textbf{2 Marks Count} &0&0&0& 0 &0&0&0&0&0
\\\hline\textbf{Total Marks} & 1&1&2&1 &1&1&\bf{1}&\bf{1.16}&\bf{2}\\\hline
\end{array}}}$$

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Recent questions in Calculus

#661
720
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3 answers
0 votes
select correct option for limit
$\lim_{x\rightarrow 0}\sin \left( \frac{1}{x}\right)$(a) 1(b) 0(c) does not exist(d) none of these
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#662
437
views
1 answers
1 votes
calculate limit
$\lim_{x\rightarrow 0}\frac{ \sin x^{\circ}}{x}$
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#663
473
views
2 answers
1 votes
calculate limit
$\lim_{x\rightarrow 0} \left( \frac{1}{x^{2}} -\frac{1}{\sin^{2}x} \right)$
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#664
861
views
2 answers
0 votes
calculate limit
$\lim_{\theta \rightarrow 0} \frac{ 1-\cos \theta }{ \theta \sin\theta }$
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#665
568
views
2 answers
1 votes
calculate limit
$\lim_{x\rightarrow 0} \frac{e^{x}-e^{\sin x}} {x-\sin x}$
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#666
476
views
2 answers
0 votes
calculate limit
$\lim_{x\rightarrow \infty }\frac{\sin x}{x}$
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#667
812
views
2 answers
0 votes
calculate limit
$\lim_{x\rightarrow 0} \frac{x^{x}-1}{x}$
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#668
367
views
2 answers
0 votes
calculate limit
$\lim_{x\rightarrow 0} \frac{6^{x}-2^{x}-3^{x}+1}{x^{2}}$
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#669
344
views
1 answers
0 votes
calculate limit
$\lim_{x\rightarrow 0}\frac{1^{x}+2^{x}+3^{x}+ \dots +n^{x}-n}{x}$
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#670
957
views
3 answers
1 votes
calculate limit
$\lim_{x\rightarrow \infty }\left(4^{x}+5^{x}\right)^{1/x}$
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#671
361
views
1 answers
0 votes
calculate limit
$\lim_{x\rightarrow \infty }x^{m}e^{-x}$ where m is +ve integer
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#672
539
views
3 answers
0 votes
calculate limit
$\lim_{x\rightarrow 0}\left ( \frac{a^{x}+b^{x}}{2} \right )^{^{\frac{1}{x}}}$
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#673
433
views
2 answers
0 votes
calculate limit
$\lim_{x\rightarrow \frac{\pi}{4}} (\tan x)^{\tan 2x}$
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#674
814
views
3 answers
1 votes
calculate limit
$\lim_{x\rightarrow \frac{\pi}{2}}{( \sin x)}^{\tan x}$
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#675
1.1k
views
1 answers
1 votes
Integration
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#676
459
views
1 answers
0 votes
CALCULUS
1/(2+e^(1/(x-3))) Is it continuous? where 2<e<3
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#677
347
views
0 answers
0 votes
Limits
Find lim x->infinity[5th root(25-24)-x]a)-1/5b)1/5c)&pi;/4d)None
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#678
2.8k
views
4 answers
0 votes
Limits
What is $\lim_{ x \to 0} (1-x)^{\frac{1}{x}}$ ? Also please explain the result?
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#679
8.4k
views
1 answers
43 votes
GATE CSE 2015 Set 3 | Question: 45
If for non-zero $x, \: af(x) + bf(\frac{1}{x}) = \frac{1}{x} - 25$ where $a \neq b \text{ then } \int\limits_1^2 f(x)dx$ ...
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#680
13.6k
views
6 answers
33 votes
GATE CSE 2015 Set 3 | Question: 9
The value of $\displaystyle \lim_{x \rightarrow \infty} (1+x^2)^{e^{-x}}$ is$0$\frac{1}{2}$1$\infty$
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