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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

0 votes
1 answer
61
1 votes
0 answers
62
Let f(x-y) = $\frac{f(x)}{f(y)}$ for all x,y $\epsilon$ R and f’(0) = p, f’(5) = q. Then the value of f’(-5) is q-q$\frac{p}{q}$$\frac{p^2}{q}$
10 votes
4 answers
63
The value of the following limit is ________________.$$\lim_{x \rightarrow 0^{+}} \frac{\sqrt{x}}{1-e^{2\sqrt{x}}}$$
0 votes
1 answer
65
Options Given were:(pi)/2pi-(pi)none
1 votes
1 answer
66
Dear Friends can any body tell me limit exists at 1 or not? as According to me the limit exists at 1 as both gives -1 at 1 but in madeeasy it’s given that the limit doe...
0 votes
2 answers
67
Calculus looks difficult for me. Any resources to learn calculus for GATE
0 votes
0 answers
68
What is the correct procedure to solve this limit ?
0 votes
0 answers
69
$\int_{0}^{1}\tan^{-1} (1-\frac{1}{x})$ d(x) find
0 votes
1 answer
70
What is the difference between Integration and Summation?Which one produces a greater value in the same range?
2 votes
0 answers
71
$\lim_{x\rightarrow a} f(x)^{g(x)} = e^{\lim_{x\rightarrow a}g(x)[f(x)-1]}$ Solve the below limit without using the above formula, $\lim_{x \rightarrow 0} ({\frac{sin x...
4 votes
1 answer
72
Compute without using power series expansion $\displaystyle \lim_{x \to 0} \frac{\sin x}{x}.$
4 votes
2 answers
75
Consider the following expression.$$\displaystyle \lim_{x\rightarrow-3}\frac{\sqrt{2x+22}-4}{x+3}$$The value of the above expression (rounded to 2 decimal places) is ____...
0 votes
1 answer
76
0 votes
0 answers
77
True/False Question :The function $f\left ( x \right )=cos\left ( e^{x} \right )$ is not uniformly continuous on $\mathbb{R}$.
0 votes
0 answers
78
The limit$$\underset{n\rightarrow \infty }{\lim}\:n^{2}\int_{0}^{1}\:\frac{1}{\left ( 1+x^{2} \right )^{n}}\:dx$$is equal to$1$$0$$+\infty$$1/2$
0 votes
0 answers
79
A solution for the differential equation $x’(t) + 2x(t) = \delta(t)$ with initial condition $x(\overline{0}) = 0$$e^{-2t}u(t)$$e^{2t}u(t)$$e^{-t}u(t)$$e^{t}u(t)$
3 votes
2 answers
80
The function $f(x)=x^{5}-5x^{4}+5x^{3}-1$ hasone minima and two maximatwo minima and one maximatwo minima and two maximaone minima and one maxima