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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

0 votes
3 answers
641
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
642
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
643
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
644
Integration
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0 votes
1 answer
645
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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0 votes
0 answers
646
Limits
Find lim x->infinity[5th root(25-24)-x] a)-1/5 b)1/5 c)&pi;/4 d)None
Find lim x->infinity[5th root(25-24)-x]a)-1/5b)1/5c)&pi;/4d)None
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0 votes
4 answers
647
Limits
What is $\lim_{ x \to 0} (1-x)^{\frac{1}{x}}$ ? Also please explain the result?
What is $\lim_{ x \to 0} (1-x)^{\frac{1}{x}}$ ? Also please explain the result?
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32 votes
6 answers
649
GATE CSE 2015 Set 3 | Question: 9
The value of $\displaystyle \lim_{x \rightarrow \infty} (1+x^2)^{e^{-x}}$ is $0$ $\frac{1}{2}$ $1$ $\infty$
The value of $\displaystyle \lim_{x \rightarrow \infty} (1+x^2)^{e^{-x}}$ is$0$$\frac{1}{2}$$1$$\infty$
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21 votes
2 answers
650
GATE CSE 2015 Set 1 | Question: 44
Compute the value of: $ \large \int \limits_{\frac{1}{\pi}}^{\frac{2}{\pi}}\frac{\cos(1/x)}{x^{2}}dx$
Compute the value of:$$ \large \int \limits_{\frac{1}{\pi}}^{\frac{2}{\pi}}\frac{\cos(1/x)}{x^{2}}dx$$
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32 votes
4 answers
652
GATE CSE 2015 Set 2 | Question: GA-3
Consider a function $f(x) = 1- |x| \text{ on } -1 \leq x \leq 1$. The value of $x$ at which the function attains a maximum, and the maximum value of the function are: $0, -1$ $-1, 0$ $0, 1$ $-1, 2$
Consider a function $f(x) = 1- |x| \text{ on } -1 \leq x \leq 1$. The value of $x$ at which the function attains a maximum, and the maximum value of the function are:$0, ...
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26 votes
6 answers
653
GATE CSE 2015 Set 1 | Question: 4
$\displaystyle \lim_{x\rightarrow \infty } x^{ \tfrac{1}{x}}$ is $\infty $ $0$ $1$ Not defined
$\displaystyle \lim_{x\rightarrow \infty } x^{ \tfrac{1}{x}}$ is$\infty $$0$$1$Not defined
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1 votes
2 answers
654
maths_mocktest1_12
A. 1 B. 2 C. 3 D. 4
A. 1B. 2C. 3D. 4
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0 votes
1 answer
655
Is the integral of second half i.e [π , 2π] being subtracted from that of the first[0, π] ? Is it right to do so?
If $\int \limits_0^{2 \pi} |x \: \sin x| dx=k\pi$, then the value of $k$ is equal to ______.
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0 votes
1 answer
656
2007 maths
Evaluate
Evaluate
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0 votes
1 answer
657
order and degree
The order and degree of the differential equation (A) 3 and 2 (B) 2 and 3 (C) 3 and 3 (D) 3 and 1
The order and degree of the differential equation(A) 3 and 2 (B) 2 and 3(C) 3 and 3 (D) 3 and 1
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18 votes
4 answers
658
GATE IT 2005 | Question: 35
What is the value of $\int_{0}^{2\pi}(x-\pi)^2 (\sin x) dx$ $-1$ $0$ $1$ $\pi$
What is the value of $\int_{0}^{2\pi}(x-\pi)^2 (\sin x) dx$$-1$$0$$1$$\pi$
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22 votes
5 answers
659
GATE IT 2008 | Question: 31
If $f(x)$ is defined as follows, what is the minimum value of $f(x)$ for $x \in (0, 2]$ ? $f(x) = \begin{cases} \frac{25}{8x} &\text{ when } x \leq \frac{3}{2} \\ x+ \frac{1}{x} &\text { otherwise}\end{cases}$ $2$ $2 \frac{1}{12}$ $2\frac{1}{6}$ $2\frac{1}{2}$
If $f(x)$ is defined as follows, what is the minimum value of $f(x)$ for $x \in (0, 2]$ ?$$f(x) = \begin{cases} \frac{25}{8x} &\text{ when } x \leq \frac{3}{2} \\ x+ \fr...
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