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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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Highest voted questions in Calculus

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641
ACE-calculus
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642
Simple Doubt in Integration
$\int_{- \pi }^{\pi} t^{2} \sin t \ dt$
$\int_{- \pi }^{\pi} t^{2} \sin t \ dt$
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643
Minimum value of f(x)
If f(x) is defined as follows, what is the minimum value of f(x) for x ∊ (0, 2] ?
If f(x) is defined as follows, what is the minimum value of f(x) for x ∊ (0, 2] ?
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644
Countinuity And Bounded Region
f(x) = x^ (-1/3) Show that f(x) is not countinuous in [-1,1] and not bounded [-1,1]
f(x) = x^ (-1/3)Show that f(x) isnot countinuous in [-1,1] andnot bounded [-1,1]
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645
CMI2016-B-7aiii
Consider the funciton $M$ defined as follows: $M(n) = \begin{cases} n-10 & \text{ if } n > 100 \\ M(M(n+11)) & \text{ if } n \leq 100 \end{cases}$ Compute the following$: M(87)$
Consider the funciton $M$ defined as follows:$M(n) = \begin{cases} n-10 & \text{ if } n 100 \\ M(M(n+11)) & \text{ if } n \leq 100 \end{cases}$Compute the following$: M(...
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646
JNU GATE
Correct Answer?
Correct Answer?
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647
Is partial derivatives and euler's theorem (related to partial derivatives) in syllabus?
Is partial derivatives and euler's theorem in syllabus? Please clarify if any idea.
Is partial derivatives and euler's theorem in syllabus?Please clarify if any idea.
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648
Calculus
$\lim_{x\rightarrow \pi } (1+\cos x)/\tan ^{2}x$
$\lim_{x\rightarrow \pi } (1+\cos x)/\tan ^{2}x$
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649
Itegration
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650
Gate 2016
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651
General Doubt
Qus 1 Qus 2
Qus 1Qus 2
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652
Diffrentiability+Limits
how to solve diffrentiability with standard procedure of f(a+h).
how to solve diffrentiability with standard procedure of f(a+h).
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653
TEST SERIES
Plz give solution
Plz give solution
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654
Calcus
1. f(x)=|x|+ |x+1|+ |x+2| is diffrentiable at x= 1 How it 1 Please Explain ?
1. f(x)=|x|+ |x+1|+ |x+2| is diffrentiable at x= 1 How it 1 Please Explain ?
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655
limits
$\lim_{x \to 0}x\log _x a$ $(A)0$ $(B)\log_ae$ $(C)1$ $(D)\log a$
$\lim_{x \to 0}x\log _x a$$(A)0$ $(B)\log_ae$$(C)1$ ...
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656
What is the difficulty level of Calculus questions?
I find Calculus part very difficult, what is the difficulty level of Calculus? also please let me know which part should I focus in Mathematic.
I find Calculus part very difficult, what is the difficulty level of Calculus? also please let me know which part should I focus in Mathematic.
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657
Integration
$\int_{-\infty}^{\infty} e^{-x^2}\, dx = \sqrt{\pi}$
$\int_{-\infty}^{\infty} e^{-x^2}\, dx = \sqrt{\pi}$
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3 answers
658
Limit
Can we calculate. $\textstyle \lim_{n \to \infty}\frac{2^{n}}{3^{n}}$ if yes then what is the value.
Can we calculate. $\textstyle \lim_{n \to \infty}\frac{2^{n}}{3^{n}}$ if yes then what is the value.
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659
calculus differentiation question
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660
Calculus
​​If $a=\Sigma_{n=0}^{\infty} \frac{x^{3n}}{(3n)!}, \: b=\Sigma_{n=1}^{\infty} \frac{x^{3n-2}}{(3n-2)!} $ and $c=\Sigma_{n=1}^{\infty} \frac{x^{3n-1}}{(3n-1)!} $, then the value of $(a^3+b^3+c^3-3abc)$ is 1 0 -1 -2
​​If $a=\Sigma_{n=0}^{\infty} \frac{x^{3n}}{(3n)!}, \: b=\Sigma_{n=1}^{\infty} \frac{x^{3n-2}}{(3n-2)!} $ and $c=\Sigma_{n=1}^{\infty} \frac{x^{3n-1}}{(3n-1)!} $, the...
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