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

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

0 votes
1 answer
101
Options Given were:(pi)/2pi-(pi)none
1 votes
1 answer
102
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
1 answer
103
f(x) = [$ tan ^2$ x] ( [ ] stands for greatest integer function)a) f(x) continuous at x = 0b) limit f(x) does not exist as x tend to 0c) f '(0) = 1d) f(x) not derivable ...
1 votes
2 answers
104
1 votes
2 answers
105
Evaluate the limit:$$ \lim_{x \to -3} \frac{\sqrt{2x+22}-4}{x+3}$$$\frac{1}{2}$$\frac{1}{4}$$\frac{1}{8}$$\frac{1}{16}$
0 votes
2 answers
106
Calculus looks difficult for me. Any resources to learn calculus for GATE
0 votes
0 answers
107
What is the correct procedure to solve this limit ?
1 votes
2 answers
108
4 votes
1 answer
109
It should be 1 and 3 ?? please correct me if I'm wrong.
1 votes
2 answers
110
$\displaystyle \lim_{x \rightarrow 0}\frac{1}{x^{6}} \displaystyle \int_{0}^{x^{2}}\frac{t^{2}dt}{t^{6}+1}=$?$1/4$$1/3$$1/2$$1$
36 votes
5 answers
111
Let $f(x)$ be a polynomial and $g(x)=f'(x)$ be its derivative. If the degree of $(f(x)+f(-x))$ is $10$, then the degree of $(g(x) - g(-x))$ is __________.
1 votes
3 answers
112
The limit $\underset{n \to \infty}{\lim} \left( 1- \frac{1}{n^2} \right) ^n$ equals$e^{-1}$$e^{-1/2}$$e^{-2}$$1$
1 votes
1 answer
114
0 votes
0 answers
115
$\int_{0}^{1}\tan^{-1} (1-\frac{1}{x})$ d(x) find
1 votes
2 answers
116
The value of $\underset{x \to 0}{\lim} \dfrac{\tan ^2 x – x \tan x }{\sin x}$ is$\frac{\sqrt{3}}{2}$$\frac{1}{2}$$0$None of these
1 votes
1 answer
117
Let $R$ be the triangle in the $xy$ – plane bounded by the $x$-axis, the line $y=x$, and the line $x=1$. The value of the double integral $$ \int \int_R \frac{\sin x}{x...
0 votes
1 answer
118
Let $f(x)=e^{-\big( \frac{1}{x^2-3x+2} \big) };x\in \mathbb{R} \: \: \& x \notin \{1,2\}$. Let $a=\underset{n \to 1^+}{\lim}f(x)$ and $b=\underset{x \to 1^-}{\lim} f(x)$....
0 votes
1 answer
119
What is the difference between Integration and Summation?Which one produces a greater value in the same range?
2 votes
0 answers
120
$\lim_{x\rightarrow a} f(x)^{g(x)} = e^{\lim_{x\rightarrow a}g(x)[f(x)-1]}$ Solve the below limit without using the above formula, $\lim_{x \rightarrow 0} ({\frac{sin x...