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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

2 votes
1 answer
521
$\lim_{x \to \infty}\left (\frac{1}{1-x^{2}} + \frac{2}{1-x^{2}}+\dots+\frac{x}{1-x^{2}}\right )$ is equal to(a) $0$(b) $-1/2$(c) $1/2$(d) None of the above
6 votes
1 answer
522
The value of $x$ at which $y$ is minimum for $y=x^2 -3x +1 $ is$-3/2$$3/2$$0$$-5/4$
5 votes
1 answer
523
$x=a \cos(t), y=b \sin(t)$ is the parametric form ofEllipseHyperbolaCircleParabola
0 votes
1 answer
524
maxima minima of 2^(sinx)/2^(cosx)
1 votes
1 answer
526
3 votes
2 answers
528
If f ' (x) =$\frac{8}{x^{}2+3x+4}$ and f(0) =1 then the lower and upper bounds of f(1) estimated by Langrange 's Mean Value Theorem are ___
0 votes
1 answer
529
1 votes
1 answer
530
Find the value of the following limit $$\lim_{x \to 0} x^{\sin x}$$My attempt:$$\begin{align*}\text{Let: }\\y &= \lim_{x \to 0} \Bigl [ x^{\sin x} \Bigr ]\\[1em]\text{The...
5 votes
3 answers
531
What is the least value of the function $f(x) = 2x^{2}-8x-3$ in the interval $[0, 5]$?$-15$$7$$-11$$-3$
3 votes
1 answer
533
26 votes
4 answers
534
36 votes
5 answers
535
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 __________.
3 votes
2 answers
536
A function y= 5x^2+ 10x is defined over an open interval x = (1,2). Atleast at one point in this interval, dy/dx is exactly(A) 20 (B) 25 (C) 30 (D) 35
0 votes
1 answer
539
0 votes
1 answer
540