Register

Web Page

Syllabus: Limits, Continuity, and Differentiability, Maxima and minima, Mean value theorem, Integration.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 1 &1&1&1&1&1&0&1&1&1&0&0.9&1
\\\hline\textbf{2 Marks Count} & 0 &0&0&0&0&0&1&0&0&0&0&0.1&1
\\\hline\textbf{Total Marks} & 1 &1&1&1&1&1&2&1&1&1&\bf{1}&\bf{1.1}&\bf{2}\\\hline
\end{array}}}$$

Filter

Most viewed questions in Calculus

22 votes
5 answers
21
GATE IT 2008 | Question: 31
If $f(x)$ is defined as follows, what is the minimum value of $f(x)$ for $x \in (0, 2]$ ? $f(x) = \begin{cases} \frac{25}{8x} &\text{ when } x \leq \frac{3}{2} \\ x+ \frac{1}{x} &\text { otherwise}\end{cases}$ $2$ $2 \frac{1}{12}$ $2\frac{1}{6}$ $2\frac{1}{2}$
If $f(x)$ is defined as follows, what is the minimum value of $f(x)$ for $x \in (0, 2]$ ?$$f(x) = \begin{cases} \frac{25}{8x} &\text{ when } x \leq \frac{3}{2} \\ x+ \fr...
User Avatar
21 votes
2 answers
23
GATE CSE 2015 Set 1 | Question: 44
Compute the value of: $ \large \int \limits_{\frac{1}{\pi}}^{\frac{2}{\pi}}\frac{\cos(1/x)}{x^{2}}dx$
Compute the value of:$$ \large \int \limits_{\frac{1}{\pi}}^{\frac{2}{\pi}}\frac{\cos(1/x)}{x^{2}}dx$$
User Avatar
17 votes
4 answers
24
GATE CSE 2013 | Question: 22
Which one of the following functions is continuous at $x = 3?$ $f(x) = \begin{cases} 2,&\text{if $x = 3$ } \\ x-1& \text{if $x > 3$}\\ \frac{x+3}{3}&\text{if $x < 3$ } \end{cases}$ ... $} \end{cases}$ $f(x) = \begin{cases} \frac{1}{x^3-27}&\text{if $x \neq 3$ } \end{cases}$
Which one of the following functions is continuous at $x = 3?$$f(x) = \begin{cases} 2,&\text{if $x = 3$ } \\ x-1& \text{if $x 3$}\\ \frac{x+3}{3}&\text{if $x < 3$ } \end...
User Avatar
32 votes
4 answers
25
GATE CSE 2015 Set 2 | Question: GA-3
Consider a function $f(x) = 1- |x| \text{ on } -1 \leq x \leq 1$. The value of $x$ at which the function attains a maximum, and the maximum value of the function are: $0, -1$ $-1, 0$ $0, 1$ $-1, 2$
Consider a function $f(x) = 1- |x| \text{ on } -1 \leq x \leq 1$. The value of $x$ at which the function attains a maximum, and the maximum value of the function are:$0, ...
User Avatar
26 votes
4 answers
26
GATE CSE 2016 Set 1 | Question: 3
$\lim _{x\rightarrow 4}\frac{\sin(x-4)}{x-4}=\_\_\_\_\_\_\_\_\_\_\_\_$
$$\lim _{x\rightarrow 4}\frac{\sin(x-4)}{x-4}=\_\_\_\_\_\_\_\_\_\_\_\_$$
User Avatar
35 votes
3 answers
27
GATE CSE 2000 | Question: 2.3
Let $S = \sum_{i=3}^{100} i \log_{2} i$, and $T = \int_{2}^{100} x \log_{2}x dx$. Which of the following statements is true? $S > T$ $S = T$ $S < T$ and $2S > T$ $2S ≤ T$
Let $S = \sum_{i=3}^{100} i \log_{2} i$, and $T = \int_{2}^{100} x \log_{2}x dx$.Which of the following statements is true?$S T$$S = T$$S < T$ and $2S T$$2S ≤ T$
User Avatar
11 votes
4 answers
28
GATE CSE 2022 | Question: 24
The value of the following limit is ________________. $\lim_{x \rightarrow 0^{+}} \frac{\sqrt{x}}{1-e^{2\sqrt{x}}}$
The value of the following limit is ________________.$$\lim_{x \rightarrow 0^{+}} \frac{\sqrt{x}}{1-e^{2\sqrt{x}}}$$
User Avatar
14 votes
7 answers
30
GATE CSE 2019 | Question: 13
Compute $\displaystyle \lim_{x \rightarrow 3} \frac{x^4-81}{2x^2-5x-3}$ $1$ $53/12$ $108/7$ Limit does not exist
Compute $\displaystyle \lim_{x \rightarrow 3} \frac{x^4-81}{2x^2-5x-3}$$1$$53/12$$108/7$Limit does not exist
User Avatar
4 votes
2 answers
31
GATE CSE 2021 Set 1 | Question: 20
Consider the following expression.$\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 ____...
User Avatar
18 votes
4 answers
32
GATE IT 2005 | Question: 35
What is the value of $\int_{0}^{2\pi}(x-\pi)^2 (\sin x) dx$ $-1$ $0$ $1$ $\pi$
What is the value of $\int_{0}^{2\pi}(x-\pi)^2 (\sin x) dx$$-1$$0$$1$$\pi$
User Avatar
22 votes
4 answers
34
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
User Avatar
5 votes
1 answer
36
Limit and Continuity
Evaluate the given limit : $lim_{x\rightarrow0} \ {\Large \frac{(1+x)^{\frac{1}{x}}-e}{x}}$ options : $ \\ a) \frac{e}{8} \\ b) -\frac{e}{2} \\ c)- \frac{e}{4} \\ d) 1$
Evaluate the given limit :$lim_{x\rightarrow0} \ {\Large \frac{(1+x)^{\frac{1}{x}}-e}{x}}$options :$ \\ a) \frac{e}{8} \\ b) -\frac{e}{2} \\ c)- \frac{e}{4} \\ d) 1$
User Avatar
10 votes
4 answers
37
GATE CSE 1997 | Question: 4.1
What is the maximum value of the function $f(x) = 2x^2 - 2x + 6$ in the interval $\left[0,2 \right]$? 6 10 12 5.5
What is the maximum value of the function $f(x) = 2x^2 - 2x + 6$ in the interval $\left[0,2 \right]$?610125.5
User Avatar
24 votes
3 answers
38
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$
User Avatar
26 votes
3 answers
39
GATE CSE 1995 | Question: 1.21
In the interval $[0, \pi]$ the equation $x=\cos x$ has No solution Exactly one solution Exactly two solutions An infinite number of solutions
In the interval $[0, \pi]$ the equation $x=\cos x$ has No solutionExactly one solutionExactly two solutionsAn infinite number of solutions
User Avatar
Page: