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

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 1 &1&1&1&1&1&0&1&1&1&0&0.9&1
\\\hline\textbf{2 Marks Count} & 0 &0&0&0&0&0&1&0&0&0&0&0.1&1
\\\hline\textbf{Total Marks} & 1 &1&1&1&1&1&2&1&1&1&\bf{1}&\bf{1.1}&\bf{2}\\\hline
\end{array}}}$$

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Recent questions in Calculus

7 votes
3 answers
661
TIFR CSE 2010 | Part A | Question: 3
The function $f (x) = 2.5 \log_e \left( 2 + \exp \left( x^2 - 4x + 5 \right)\right)$ attains a minimum at $x = $? $0$ $1$ $2$ $3$ $4$
The function $f (x) = 2.5 \log_e \left( 2 + \exp \left( x^2 - 4x + 5 \right)\right)$ attains a minimum at $x = $?$0$$1$$2$$3$$4$
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1 votes
3 answers
662
Please find the value of this limit
I have applied L'Hospital here. And result came up like this : $1 - \frac{1}{2} (y^{2} + y)^{-\frac{1}{2}} (2y+1)$ Then after applying limit value , result came as $-\infty$. Am I wrong ? Please correct me.
I have applied L'Hospital here. And result came up like this :$$1 - \frac{1}{2} (y^{2} + y)^{-\frac{1}{2}} (2y+1)$$Then after applying limit value , result came as $-\inf...
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1 votes
3 answers
663
Calculate the limit
$\lim_{x \to 0} \frac{\cos(x)-\log(1+x)-1+x}{\sin^2x} = ? $ Please explain the steps also
$$\lim_{x \to 0} \frac{\cos(x)-\log(1+x)-1+x}{\sin^2x} = ? $$Please explain the steps also
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2 votes
3 answers
664
limit
limx->0 (cot x)1/logx ? ans: 0(m getting 1/e)
limx->0 (cot x)1/logx ?ans: 0(m getting 1/e)
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0 votes
3 answers
665
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
$\lim_{x\rightarrow 0}\sin \left( \frac{1}{x}\right)$(a) 1(b) 0(c) does not exist(d) none of these
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1 votes
1 answer
666
calculate limit
$\lim_{x\rightarrow 0}\frac{ \sin x^{\circ}}{x}$
$\lim_{x\rightarrow 0}\frac{ \sin x^{\circ}}{x}$
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0 votes
1 answer
667
calculate limit
$\lim_{x\rightarrow 0} \left( \frac{1}{x^{2}} -\frac{1}{\sin^{2}x} \right)$
$\lim_{x\rightarrow 0} \left( \frac{1}{x^{2}} -\frac{1}{\sin^{2}x} \right)$
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0 votes
2 answers
668
calculate limit
$\lim_{\theta \rightarrow 0} \frac{ 1-\cos \theta }{ \theta \sin\theta }$
$\lim_{\theta \rightarrow 0} \frac{ 1-\cos \theta }{ \theta \sin\theta }$
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1 votes
2 answers
669
calculate limit
$\lim_{x\rightarrow 0} \frac{e^{x}-e^{\sin x}} {x-\sin x}$
$\lim_{x\rightarrow 0} \frac{e^{x}-e^{\sin x}} {x-\sin x}$
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0 votes
2 answers
670
calculate limit
$\lim_{x\rightarrow \infty }\frac{\sin x}{x}$
$\lim_{x\rightarrow \infty }\frac{\sin x}{x}$
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0 votes
2 answers
671
calculate limit
$\lim_{x\rightarrow 0} \frac{x^{x}-1}{x}$
$\lim_{x\rightarrow 0} \frac{x^{x}-1}{x}$
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0 votes
2 answers
672
calculate limit
$\lim_{x\rightarrow 0} \frac{6^{x}-2^{x}-3^{x}+1}{x^{2}}$
$\lim_{x\rightarrow 0} \frac{6^{x}-2^{x}-3^{x}+1}{x^{2}}$
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0 votes
1 answer
673
calculate limit
$\lim_{x\rightarrow 0}\frac{1^{x}+2^{x}+3^{x}+ \dots +n^{x}-n}{x}$
$\lim_{x\rightarrow 0}\frac{1^{x}+2^{x}+3^{x}+ \dots +n^{x}-n}{x}$
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1 votes
3 answers
674
calculate limit
$\lim_{x\rightarrow \infty }\left(4^{x}+5^{x}\right)^{1/x}$
$\lim_{x\rightarrow \infty }\left(4^{x}+5^{x}\right)^{1/x}$
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0 votes
1 answer
675
calculate limit
$\lim_{x\rightarrow \infty }x^{m}e^{-x}$ where m is +ve integer
$\lim_{x\rightarrow \infty }x^{m}e^{-x}$ where m is +ve integer
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0 votes
3 answers
676
calculate limit
$\lim_{x\rightarrow 0}\left ( \frac{a^{x}+b^{x}}{2} \right )^{^{\frac{1}{x}}}$
$\lim_{x\rightarrow 0}\left ( \frac{a^{x}+b^{x}}{2} \right )^{^{\frac{1}{x}}}$
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0 votes
2 answers
677
calculate limit
$\lim_{x\rightarrow \frac{\pi}{4}} (\tan x)^{\tan 2x}$
$\lim_{x\rightarrow \frac{\pi}{4}} (\tan x)^{\tan 2x}$
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1 votes
3 answers
678
calculate limit
$\lim_{x\rightarrow \frac{\pi}{2}}{( \sin x)}^{\tan x}$
$\lim_{x\rightarrow \frac{\pi}{2}}{( \sin x)}^{\tan x}$
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1 votes
1 answer
679
Integration
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0 votes
1 answer
680
CALCULUS
1/(2+e^(1/(x-3))) Is it continuous? where 2<e<3
1/(2+e^(1/(x-3))) Is it continuous? where 2<e<3
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