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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

2 votes
0 answers
121
#calculus #limits
$\lim_{x\rightarrow a} f(x)^{g(x)} = e^{\lim_{x\rightarrow a}g(x)[f(x)-1]}$ Solve the below limit without using the above formula, $\lim_{x \rightarrow 0} ({\frac{sin x}{x}})^{\frac{sin x}{x - sin x}}$
$\lim_{x\rightarrow a} f(x)^{g(x)} = e^{\lim_{x\rightarrow a}g(x)[f(x)-1]}$ Solve the below limit without using the above formula, $\lim_{x \rightarrow 0} ({\frac{sin x...
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0 votes
1 answer
122
ISI2016-DCG-56
$\underset{x\rightarrow \infty}{\lim} \left(1+\dfrac{1}{x^{2}}\right)^{x}$ equals $-1$ $0$ $1$ Does not exist
$\underset{x\rightarrow \infty}{\lim} \left(1+\dfrac{1}{x^{2}}\right)^{x}$ equals$-1$$0$$1$Does not exist
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5 votes
3 answers
123
ISI2004-MIII: 13
Let $X =\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+\ldots+\frac{1}{3001}$. Then $X< 1$ $X>\frac{3}{2}$ $1< X< \frac{3}{2}$ none of the above
Let $X =\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+\ldots+\frac{1}{3001}$. Then$X< 1$$X>\frac{3}{2}$$1< X< \frac{3}{2}$none of the above
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1 votes
1 answer
124
ISI2015-DCG-56
$\underset{x \to \infty}{\lim} \left( 1 + \dfrac{1}{x^2} \right) ^x$ equals $-1$ $0$ $1$ Does not exist
$\underset{x \to \infty}{\lim} \left( 1 + \dfrac{1}{x^2} \right) ^x$ equals$-1$$0$$1$Does not exist
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1 votes
1 answer
126
me book mathematics
Which of following function is strictly bounded?
Which of following function is strictly bounded?
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0 votes
1 answer
127
Gilbert Strang
$\int_{}^{}\frac{x dx}{\sqrt{x^4-1}}$
$\int_{}^{}\frac{x dx}{\sqrt{x^4-1}}$
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28 votes
4 answers
128
GATE CSE 2018 | Question: 16
The value of $\int^{\pi/4} _0 x \cos(x^2) dx$ correct to three decimal places (assuming that $\pi = 3.14$) is ____
The value of $\int^{\pi/4} _0 x \cos(x^2) dx$ correct to three decimal places (assuming that $\pi = 3.14$) is ____
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31 votes
5 answers
131
GATE CSE 2014 Set 3 | Question: 6
If $\int \limits_0^{2 \pi} |x \: \sin x| dx=k\pi$, then the value of $k$ is equal to ______.
If $\int \limits_0^{2 \pi} |x \: \sin x| dx=k\pi$, then the value of $k$ is equal to ______.
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1 votes
3 answers
132
ISRO2006-ECE calculus
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24 votes
3 answers
133
GATE CSE 2009 | Question: 25
$\int^{\pi/4}_0 (1-\tan x)/(1+\tan x)\,dx $ $0$ $1$ $\ln 2$ $1/2 \ln 2$
$\int^{\pi/4}_0 (1-\tan x)/(1+\tan x)\,dx $$0$$1$ $\ln 2$$1/2 \ln 2$
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0 votes
2 answers
134
ISRO 2009-ECE Engineering Mathematics
There is a function f(x), such that f(0) = 1 and f ' (0)= -1 and f(x) is positive for all values of x. Then, a) f"(x) < 0 for all x b) -1 < f'' (x) < 0 for all x c) -2 < f '' (x) < -1 for all x d) None of the above
There is a function f(x), such that f(0) = 1 and f ' (0)= -1 and f(x) is positive for all values of x. Then,a) f"(x) < 0 for all xb) -1 < f'' (x) < 0 for all xc) -2 < f ...
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9 votes
2 answers
135
ISI2004-MIII: 12
The maximum possible value of $xy^2z^3$ subjected to condition $x,y,z \geq 0$ and $x+y+z=3$ is $1$ $\frac{9}{8}$ $\frac{9}{4}$ $\frac{27}{16}$
The maximum possible value of $xy^2z^3$ subjected to condition $x,y,z \geq 0$ and $x+y+z=3$ is$1$$\frac{9}{8}$$\frac{9}{4}$$\frac{27}{16}$
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2 votes
2 answers
136
Gate 2014 CE Set 2
The expression $\lim_{a \to 0}\frac{x^{a}-1}{a}$ is equal to (A)$\log x$ (B)0 (c)$x\log x$ (D)$\infty$
The expression $\lim_{a \to 0}\frac{x^{a}-1}{a}$ is equal to (A)$\log x$ (B)0 (c)$x\log x$ (D)$\infty$
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3 votes
2 answers
139
GATE Overflow Test Series | Mock GATE | Test 3 | Question: 59
If the function $f(x) =\left\{ \begin{array}{rcl} \alpha \sqrt{x+1} &;0\leq x \leq 3 \\\beta x + 2&;3 < x\leq 5\end{array}\right.$ is differentiable, then the value of $\alpha - \beta$ is _________
If the function $f(x) =\left\{ \begin{array}{rcl} \alpha \sqrt{x+1} &;0\leq x \leq 3 \\\beta x + 2&;3 < x\leq 5\end{array}\right.$ is differentiable, then the value of $\...
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8 votes
1 answer
140
GATE Overflow Test Series | Mock GATE | Test 2 | Question: 18
The minimum value of the function $f(x) = \frac{x^2}{2} - x$ occurs at (Mark all the appropriate choices) $x = -1$ $x = 1$ $x = 0$ $ x = \frac{1}{\sqrt{2}}$
The minimum value of the function $$f(x) = \frac{x^2}{2} - x$$ occurs at (Mark all the appropriate choices)$x = -1$$x = 1$$x = 0$$ x = \frac{1}{\sqrt{2}}$
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