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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

3 votes
2 answers
512
Calculus
Can anyone tell me range of f(x)=|sinx|+|cosx|
Can anyone tell me range of f(x)=|sinx|+|cosx|
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0 votes
1 answer
513
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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10 votes
1 answer
514
ISRO2016-3
$\displaystyle{}\lim_{x\rightarrow 0}\frac{\sqrt{1+x}-\sqrt{1-x}}{x}$ is given by $0$ $-1$ $1$ $\frac{1}{2}$
$\displaystyle{}\lim_{x\rightarrow 0}\frac{\sqrt{1+x}-\sqrt{1-x}}{x}$ is given by$0$$-1$$1$$\frac{1}{2}$
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0 votes
1 answer
515
What is the difficulty level of Calculus questions?
I find Calculus part very difficult, what is the difficulty level of Calculus? also please let me know which part should I focus in Mathematic.
I find Calculus part very difficult, what is the difficulty level of Calculus? also please let me know which part should I focus in Mathematic.
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0 votes
0 answers
516
Integration
$\int_{-\infty}^{\infty} e^{-x^2}\, dx = \sqrt{\pi}$
$\int_{-\infty}^{\infty} e^{-x^2}\, dx = \sqrt{\pi}$
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0 votes
3 answers
517
Limit
Can we calculate. $\textstyle \lim_{n \to \infty}\frac{2^{n}}{3^{n}}$ if yes then what is the value.
Can we calculate. $\textstyle \lim_{n \to \infty}\frac{2^{n}}{3^{n}}$ if yes then what is the value.
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5 votes
1 answer
518
ISRO2011-59
$n$-th derivative of $x^n$ is $nx^{n-1}$ $n^n.n!$ $nx^n!$ $n!$
$n$-th derivative of $x^n$ is$nx^{n-1}$$n^n.n!$$nx^n!$$n!$
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0 votes
0 answers
519
calculus differentiation question
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0 votes
0 answers
520
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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2 votes
1 answer
521
calculus
$\lim_{x \to \infty}\left (\frac{1}{1-x^{2}} + \frac{2}{1-x^{2}}+\dots+\frac{x}{1-x^{2}}\right )$ is equal to (a) $0$ (b) $-1/2$ (c) $1/2$ (d) None of the above
$\lim_{x \to \infty}\left (\frac{1}{1-x^{2}} + \frac{2}{1-x^{2}}+\dots+\frac{x}{1-x^{2}}\right )$ is equal to(a) $0$(b) $-1/2$(c) $1/2$(d) None of the above
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6 votes
1 answer
522
ISRO2009-50
The value of $x$ at which $y$ is minimum for $y=x^2 -3x +1 $ is $-3/2$ $3/2$ $0$ $-5/4$
The value of $x$ at which $y$ is minimum for $y=x^2 -3x +1 $ is$-3/2$$3/2$$0$$-5/4$
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5 votes
1 answer
523
ISRO2009-49
$x=a \cos(t), y=b \sin(t)$ is the parametric form of Ellipse Hyperbola Circle Parabola
$x=a \cos(t), y=b \sin(t)$ is the parametric form ofEllipseHyperbolaCircleParabola
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0 votes
1 answer
524
maxima minima
maxima minima of 2^(sinx)/2^(cosx)
maxima minima of 2^(sinx)/2^(cosx)
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1 votes
1 answer
526
limits
Let $f(x,y) = \begin{cases} 1, & \quad if \: xy=0, \\ xy, & \quad xy \neq 0. \end{cases}$ Then $f$ is continuous at $(0,0)$ and $\frac{\partial f}{ \partial x} (0,0)$ exists $f$ is not continuous at $(0,0)$ ... $f$ is not continuous at $(0,0)$ and $\frac{\partial f}{ \partial x} (0,0)$ does not exist
Let $f(x,y) = \begin{cases} 1, & \quad if \: xy=0, \\ xy, & \quad xy \neq 0. \end{cases}$Then$f$ is continuous at $(0,0)$ and $\frac{\partial f}{ \partial x} (0,0)$ exist...
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3 votes
2 answers
528
Lagrange 's Mean Value Theorem 2
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 ___
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 ___
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0 votes
1 answer
529
Lagrange 's Mean Value Theorem
Question: The value of $\zeta$ of $f(b) - f(a) = (b-a) \cdot f'(\zeta)$ for the function $f(x) = Ax^2 + Bx +C$ in the interval $[a,b]$ is _______ My Attempt : STEP 1: $f(x)$ is polynomial function therefore continuous STEP 2: $f(x)$ is ... How to proceed further?
Question:The value of $\zeta$ of $f(b) - f(a) = (b-a) \cdot f'(\zeta)$ for the function $f(x) = Ax^2 + Bx +C$ in the interval $[a,b]$ is _______My Attempt :STEP 1: $f(x)...
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1 votes
1 answer
530
Limit of Logarithematic and Exponentials
Find the value of the following limit $\lim_{x \to 0} x^{\sin x}$ ... $0 \cdot \infty$ form now? How do I proceed further?
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...
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