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

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

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Most viewed questions in Calculus

3 votes
2 answers
211
Limits Indeterminate forms
$\lim_{x \rightarrow 0^{+}} x^{\frac{1}{\ln x}}$
$\lim_{x \rightarrow 0^{+}} x^{\frac{1}{\ln x}}$
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2 votes
1 answer
212
Calculus Limit
Find the value of Here I got till $lim_{x \rightarrow \infty} \frac{4^2 + \frac{3^x}{4^x}}{4^{-2}}$. But how to proceed further?
Find the value of Here I got till $lim_{x \rightarrow \infty} \frac{4^2 + \frac{3^x}{4^x}}{4^{-2}}$. But how to proceed further?
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0 votes
1 answer
213
funtion
suppose a set A= { x/x ∈ N and X< 9 } and set B ={ x/x+5 = 8 and X∈ N } 1) how many one to one funtions are possible from set B to A 2) how many on to funtions are possible from set A to B
suppose a set A= { x/x ∈ N and X< 9 } and set B ={ x/x+5 = 8 and X∈ N }1) how many one to one funtions are possible from set B to A2) how many on to funtions are po...
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2 votes
2 answers
214
ISI2016-MMA-8
Let $g: \mathbb{R} \rightarrow \mathbb{R}$ be differentiable with $g'(x^2)=x^3$ for all $x>0$ and $g(1) =1$. Then $g(4)$ equals $64/5$ $32/5$ $37/5$ $67/5$
Let $g: \mathbb{R} \rightarrow \mathbb{R}$ be differentiable with $g'(x^2)=x^3$ for all $x>0$ and $g(1) =1$. Then $g(4)$ equals$64/5$$32/5$$37/5$$67/5$
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1 votes
3 answers
215
calculate limit
$\lim_{x\rightarrow \infty }\left(4^{x}+5^{x}\right)^{1/x}$
$\lim_{x\rightarrow \infty }\left(4^{x}+5^{x}\right)^{1/x}$
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1 votes
2 answers
216
Applied Mathematics Calculus and Limit Question
Evaluate the question of the following limits. $\lim_{x\rightarrow 1} \frac{x}{(x-1)^{2}}$
Evaluate the question of the following limits. $\lim_{x\rightarrow 1} \frac{x}{(x-1)^{2}}$
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0 votes
2 answers
218
ISI2015-DCG-47
The Taylor series expansion of $f(x)= \text{ln}(1+x^2)$ about $x=0$ is $\sum _{n=1}^{\infty} (-1)^n \frac{x^n}{n}$ $\sum _{n=1}^{\infty} (-1)^{n+1} \frac{x^{2n}}{n}$ $\sum _{n=1}^{\infty} (-1)^{n+1} \frac{x^{2n+1}}{n+1}$ $\sum _{n=0}^{\infty} (-1)^{n+1} \frac{x^{n+1}}{n+1}$
The Taylor series expansion of $f(x)= \text{ln}(1+x^2)$ about $x=0$ is$\sum _{n=1}^{\infty} (-1)^n \frac{x^n}{n}$$\sum _{n=1}^{\infty} (-1)^{n+1} \frac{x^{2n}}{n}$$\sum _...
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1 votes
2 answers
221
maths_mocktest1_12
A. 1 B. 2 C. 3 D. 4
A. 1B. 2C. 3D. 4
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1 votes
1 answer
224
Area Bounded By Curve
Let f(x)=x−(1/2) and A denote the area of region bounded by f(x) and the x-axis, when x varies from -1 to 1. A is nonzero and finite??
Let f(x)=x−(1/2) and A denote the area of region bounded by f(x) and the x-axis, when x varies from -1 to 1.A is nonzero and finite??
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1 votes
2 answers
227
GATE DS&AI 2024 | Question: 50
Evaluate the following limit: \[ \lim _{x \rightarrow 0} \frac{\ln \left(\left(x^{2}+1\right) \cos x\right)}{x^{2}}= \]
Evaluate the following limit:\[\lim _{x \rightarrow 0} \frac{\ln \left(\left(x^{2}+1\right) \cos x\right)}{x^{2}}= \]
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3 votes
3 answers
228
solve calculate the limit
$\lim_{n \to \infty} \left [ \frac{1}{(1+n)} + \frac{1}{(2+n)} + - - - - - + \frac{1}{(n+n)} \right ]$ a) $log 2$ b) $2$ c) $\frac{1}{2}$ d) $\Pi /4$
$\lim_{n \to \infty} \left [ \frac{1}{(1+n)} + \frac{1}{(2+n)} + - - - - - + \frac{1}{(n+n)} \right ]$a) $log 2$ b) $2$c) $\frac{1}{2}$ ...
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0 votes
1 answer
229
Maxima and Minima
Find the stationary points, maxima and minima f(x)=|x+1|+|x-1| , -3<=x<=2
Find the stationary points, maxima and minimaf(x)=|x+1|+|x-1| , -3<=x<=2
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