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

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

Recent questions in Calculus

1 votes
1 answer
501
someone plz give solution
4 votes
1 answer
502
Let $\frac{d}{dx} [f(x)] = \frac{e^{sinx}}{x} , x 0 .$If $\int_{1}^{4}(\frac{2e^{sinx^{2}}}{x}) dx = f(k) - f(1)$ where limits of integration is from $1$ to $4$ , then $...
2 votes
2 answers
503
How to slove this$\lim_{n\rightarrow \infty }\left ( 10^{n}+n^{20} \right )/n!$
0 votes
1 answer
504
Plz give solution
1 votes
3 answers
505
2 votes
1 answer
506
Calculate the limit$\lim_{x \rightarrow 1-} \sqrt[3]{x+1} \: ln \: (x+1)$102Does not exist
1 votes
1 answer
507
3 votes
2 answers
508
what is the value of$\textstyle \lim_{x \to 2}\frac{x-2}{\log(x-1)}$
0 votes
1 answer
509
1. f(x)=|x|+ |x+1|+ |x+2| is diffrentiable at x= 1 How it 1 Please Explain ?
2 votes
2 answers
510
The expression $\lim_{a \to 0}\frac{x^{a}-1}{a}$ is equal to (A)$\log x$ (B)0 (c)$x\log x$ (D)$\infty$
3 votes
2 answers
512
Can anyone tell me range of f(x)=|sinx|+|cosx|
0 votes
1 answer
513
$\lim_{x \to 0}x\log _x a$$(A)0$ $(B)\log_ae$$(C)1$ ...
10 votes
1 answer
514
$\displaystyle{}\lim_{x\rightarrow 0}\frac{\sqrt{1+x}-\sqrt{1-x}}{x}$ is given by$0$$-1$$1$$\frac{1}{2}$
0 votes
1 answer
515
I find Calculus part very difficult, what is the difficulty level of Calculus? also please let me know which part should I focus in Mathematic.
0 votes
0 answers
516
$\int_{-\infty}^{\infty} e^{-x^2}\, dx = \sqrt{\pi}$
0 votes
3 answers
517
Can we calculate. $\textstyle \lim_{n \to \infty}\frac{2^{n}}{3^{n}}$ if yes then what is the value.
5 votes
1 answer
518
$n$-th derivative of $x^n$ is$nx^{n-1}$$n^n.n!$$nx^n!$$n!$
0 votes
0 answers
519
0 votes
0 answers
520
​​If $a=\Sigma_{n=0}^{\infty} \frac{x^{3n}}{(3n)!}, \: b=\Sigma_{n=1}^{\infty} \frac{x^{3n-2}}{(3n-2)!} $ and $c=\Sigma_{n=1}^{\infty} \frac{x^{3n-1}}{(3n-1)!} $, the...