Web Page

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

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

Highest voted questions in Calculus

4 votes
1 answer
92
​​​​​Let $f(x)$ be a continuous function from $\mathbb{R}$ to $\mathbb{R}$ such that\[f(x)=1-f(2-x)\]Which one of the following options is the CORRECT value of ...
4 votes
1 answer
95
Compute without using power series expansion $\displaystyle \lim_{x \to 0} \frac{\sin x}{x}.$
4 votes
2 answers
96
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 ____...
4 votes
4 answers
97
$\underset{x \to \infty}{\lim} \left( \frac{3x-1}{3x+1} \right) ^{4x}$ equals$1$$0$$e^{-8/3}$$e^{4/9}$
4 votes
0 answers
100
What is the value of $\displaystyle \lim_{x\to \infty} \left(\frac{x}{2+x}\right)^{2x}?$
4 votes
1 answer
101
It should be 1 and 3 ?? please correct me if I'm wrong.
4 votes
1 answer
102
Value of an Integral :I = $\frac{1}{\sqrt{2\Pi }} \int_{0}^{\infty } e^{\frac{-x^{2}}{8}}dx$Answer given is 1.
4 votes
5 answers
103
4 votes
2 answers
104
Find the coefficient of x10$\left ( 1+x^{2}+x^{4}+........ \right )\left ( 1+x^{4}+x^{8}+..... \right )\left ( 1+x^{6}+x^{12}..... \right )$
4 votes
1 answer
106
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 $...
4 votes
2 answers
107
$\lim_{x \rightarrow \infty} \left(\frac{x^{2} + 5x +3}{x^{2} + x + 2}\right)^{x}$
4 votes
1 answer
108
4 votes
1 answer
110
Please solve the following integration problem$\int_{0}^{\infty}{ y^{\frac{1}{2} }}e^{-y^3}dx$I want full explanation. please help me ?