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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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Recent questions in Calculus

22 votes
4 answers
461
GATE CSE 2017 Set 1 | Question: 28
The value of $\displaystyle \lim_{x\rightarrow 1} \frac{x^{7}-2x^{5}+1}{x^{3}-3x^{2}+2}$ is $0$ is $-1$ is $1$ does not exist
The value of $\displaystyle \lim_{x\rightarrow 1} \frac{x^{7}-2x^{5}+1}{x^{3}-3x^{2}+2}$is $0$is $-1$is $1$does not exist
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2 votes
0 answers
463
Integration doubt
How to integrate: $\int e^{-x^{2}} dx$ More specifically, how to integrate standard normal distribution function from 0 to a?
How to integrate: $\int e^{-x^{2}} dx$More specifically, how to integrate standard normal distribution function from 0 to a?
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0 votes
0 answers
464
Basic Calculus
what is the difference between Local maxima/minima and absolute maxima/minima ???? example would be great
what is the difference between Local maxima/minima and absolute maxima/minima ???? example would be great
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0 votes
1 answer
465
Virtual Gate
Calculate the limit (A) 1 (B) 0 (C) -1 (D) Does not exist
Calculate the limit (A) 1 (B) 0 (C) -1 (D) Does not exist
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1 votes
1 answer
466
LIMIT
$\lim_{X\rightarrow \infty } -(x+1)(e^{\frac{1}{x+1}}-1)$
$\lim_{X\rightarrow \infty } -(x+1)(e^{\frac{1}{x+1}}-1)$
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0 votes
1 answer
467
how to integrate this
$\int_{1}^{n}\frac{dt}{log (t)}$
$\int_{1}^{n}\frac{dt}{log (t)}$
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2 votes
0 answers
468
How to integrate this
$\int_{1}^{n} \frac{u^{-1/3}}{log u} du$
$\int_{1}^{n} \frac{u^{-1/3}}{log u} du$
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1 votes
0 answers
469
VirtualGATE2017-1
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0 votes
2 answers
470
Integration
what is the integration of this funcion? f(x)=1−|x| where −1≤x≤1
what is the integration of this funcion? f(x)=1−|x| where −1≤x≤1
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2 votes
3 answers
472
Integration
Solve the following $\int_{0}^{\infty}e^{-x^2}x^4dx$
Solve the following $\int_{0}^{\infty}e^{-x^2}x^4dx$
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0 votes
1 answer
473
Test Series
https://gateoverflow.in/?qa=blob&qa_blobid=4549376166631720003
https://gateoverflow.in/?qa=blob&qa_blobid=4549376166631720003
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1 votes
1 answer
474
Definite Integration
Let $\frac{\mathrm{d} }{\mathrm{d} x}f(x)$ = $\frac{e^{sinx}}{x}, x>0$ if $\int_{1}^{4}\frac{2e^{sinx^{2}}}{x}d(x)$ = f(k)-f(1) then k = ______
Let $\frac{\mathrm{d} }{\mathrm{d} x}f(x)$ = $\frac{e^{sinx}}{x}, x>0$ if $\int_{1}^{4}\frac{2e^{sinx^{2}}}{x}d(x)$ = f(k)-f(1) then k = ______
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0 votes
1 answer
475
ACE-calculus
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2 votes
1 answer
476
Simple Integration Q2
$\int_{0}^{\frac{\pi}{4}}( \sec 2x -\tan 2x )\ dx$
$\int_{0}^{\frac{\pi}{4}}( \sec 2x -\tan 2x )\ dx$
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0 votes
1 answer
477
Simple Doubt in Integration
$\int_{- \pi }^{\pi} t^{2} \sin t \ dt$
$\int_{- \pi }^{\pi} t^{2} \sin t \ dt$
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0 votes
0 answers
478
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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0 votes
0 answers
479
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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1 votes
2 answers
480
CMI2016-B-7ai
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$: M(101)$
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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