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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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Hot questions in Calculus

0 votes
2 answers
91
Applied Mathematics Calculus and Limit Question
Evaluate the question of the following limits. $\lim_{x\rightarrow \infty} \frac{2x^{3}+3x-5}{5x^{3}+1}$
Evaluate the question of the following limits. $\lim_{x\rightarrow \infty} \frac{2x^{3}+3x-5}{5x^{3}+1}$
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0 votes
1 answer
92
Applied Mathematics Derivative
Please find derivation of the following equation. Let $f(x)=e^{x^{2}}\ln x,$ then find, ${f}'(x)$.
Please find derivation of the following equation.Let $f(x)=e^{x^{2}}\ln x,$ then find, ${f}'(x)$.
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4 votes
2 answers
93
GATE CSE 2021 Set 1 | Question: 20
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 ___________.
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 ____...
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16 votes
3 answers
94
GATE CSE 1993 | Question: 02.1
$\displaystyle \lim_{x \to 0} \frac{x(e^x - 1) + 2(\cos x -1)}{x(1 - \cos x)}$ is __________
$\displaystyle \lim_{x \to 0} \frac{x(e^x - 1) + 2(\cos x -1)}{x(1 - \cos x)}$ is __________
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0 votes
1 answer
96
ISI2015-MMA-73
$f(x)$ is a differentiable function on the real line such that $\underset{x \to \infty=}{\lim} f(x) =1$ and $\underset{x \to \infty=}{\lim} f’(x) =\alpha$. Then $\alpha$ must be $0$ $\alpha$ need not be $0$, but $\mid \alpha \mid <1$ $\alpha >1$ $\alpha < -1$
$f(x)$ is a differentiable function on the real line such that $\underset{x \to \infty=}{\lim} f(x) =1$ and $\underset{x \to \infty=}{\lim} f’(x) =\alpha$. Then$\alpha$...
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0 votes
0 answers
97
iit kanpur Calculas practice question
Does there exist a differentiable function f : [0, 2] → R satisfying f(0) = −1, f(2) = 4 and f’(x) ≤ 2 for all x ∈ [0, 2]?
Does there exist a differentiable function f : [0, 2] → R satisfying f(0) = −1, f(2) = 4 and f’(x) ≤ 2 for all x ∈ [0, 2]?
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0 votes
1 answer
98
Calculus by Spivak 4th edition Chapter 10 problem 9
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3 votes
2 answers
99
NIELIT 2016 MAR Scientist B - Section B: 5
The greatest and the least value of $f(x)=x^4-8x^3+22x^2-24x+1$ in $[0,2]$ are $0,8$ $0,-8$ $1,8$ $1,-8$
The greatest and the least value of $f(x)=x^4-8x^3+22x^2-24x+1$ in $[0,2]$ are$0,8$$0,-8$$1,8$$1,-8$
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1 votes
0 answers
100
#ISI2021
Let f(x-y) = $\frac{f(x)}{f(y)}$ for all x,y $\epsilon$ R and f’(0) = p, f’(5) = q. Then the value of f’(-5) is q -q $\frac{p}{q}$ $\frac{p^2}{q}$
Let f(x-y) = $\frac{f(x)}{f(y)}$ for all x,y $\epsilon$ R and f’(0) = p, f’(5) = q. Then the value of f’(-5) is q-q$\frac{p}{q}$$\frac{p^2}{q}$
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0 votes
1 answer
102
Made Easy Full length Test
Options Given were: (pi)/2 pi -(pi) none
Options Given were:(pi)/2pi-(pi)none
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1 votes
1 answer
103
Made Easy Test Series Engineering Maths
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 doesn’t exists...
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...
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0 votes
1 answer
104
ISRO 2009- ECE Calculus
f(x) = [$ tan ^2$ x] ( [ ] stands for greatest integer function) a) f(x) continuous at x = 0 b) limit f(x) does not exist as x tend to 0 c) f '(0) = 1 d) f(x) not derivable at x = 0
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 ...
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1 votes
2 answers
105
NIELIT 2016 MAR Scientist B - Section B: 13
$\underset{x\to 0}{\lim} \dfrac{(1-\cos x)}{2}$ is equal to $0$ $1$ $1/3$ $1/2$
$\underset{x\to 0}{\lim} \dfrac{(1-\cos x)}{2}$ is equal to$0$$1$$1/3$$1/2$
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1 votes
2 answers
106
GATE Overflow | Mock GATE | Test 1 | Question: 19
Evaluate the limit: $ \lim_{x \to -3} \frac{\sqrt{2x+22}-4}{x+3}$ $\frac{1}{2}$ $\frac{1}{4}$ $\frac{1}{8}$ $\frac{1}{16}$
Evaluate the limit:$$ \lim_{x \to -3} \frac{\sqrt{2x+22}-4}{x+3}$$$\frac{1}{2}$$\frac{1}{4}$$\frac{1}{8}$$\frac{1}{16}$
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0 votes
2 answers
107
Calculus self doubt
Calculus looks difficult for me. Any resources to learn calculus for GATE
Calculus looks difficult for me. Any resources to learn calculus for GATE
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37 votes
5 answers
108
GATE CSE 2016 Set 2 | Question: 02
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 __________.
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 __________.
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0 votes
0 answers
109
Applied Test Series
What is the correct procedure to solve this limit ?
What is the correct procedure to solve this limit ?
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1 votes
2 answers
110
NIELIT 2016 MAR Scientist B - Section B: 11
What is the derivative w.r.t $x$ of the function given by $\large \Phi(x)= \displaystyle \int_{0}^{x^2}\sqrt t\:dt$, $2x^2$ $\sqrt x$ $0$ $1$
What is the derivative w.r.t $x$ of the function given by$\large \Phi(x)= \displaystyle \int_{0}^{x^2}\sqrt t\:dt$,$2x^2$$\sqrt x$$0$$1$
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