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

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Recent questions in Calculus
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1
GATEBOOK2019Calculus11
Evaluation of the integral $\int_0^{\frac{\pi}{8}} \cos^5 4x dx$ gives $\frac{1}{15}$ $\frac{1}{8}$ $\frac{7}{15}$ $\frac{2}{15}$
asked
Dec 23, 2018
in
Calculus
by
Arjun
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364k
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gb2019calculus1
numericalanswers
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1
answer
2
GATEBOOK2019Calculus12
If $\lim_{x \rightarrow 0} \frac{\cos 4x + a \cos 2x+b}{x^4}$ is finite, then the values of $a, b$ are respectively. $5, 4$ $5, 4$ $4, 3$ $4, 3$
asked
Dec 23, 2018
in
Calculus
by
Arjun
Veteran
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364k
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gb2019calculus1
0
votes
1
answer
3
GATEBOOK2019Calculus13
If a triangle $ABC$ has vertex points $A(0,0), B(1, 0)$ and $C(0, 1)$, then the value of integral $\int \: \int 3y dxdy$ evaluated over the triangle is $\frac{1}{2}$ $\frac{1}{4}$ $\frac{1}{8}$ $\frac{1}{16}$
asked
Dec 23, 2018
in
Calculus
by
Arjun
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364k
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gb2019calculus1
0
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1
answer
4
GATEBOOK2019Calculus14
The value of integral $\int_1^3 \frac{\mid x2 \mid}{x} \: dx$ is ____
asked
Dec 23, 2018
in
Calculus
by
Arjun
Veteran
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364k
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1
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gb2019calculus1
numericalanswers
0
votes
1
answer
5
GATEBOOK2019Calculus15
$\lim_{n \rightarrow \infty} (2n^4)^{\frac{1}{3n}} =$ $e$ $1$ $2^{\frac{1}{3}}$ $0$
asked
Dec 23, 2018
in
Calculus
by
Arjun
Veteran
(
364k
points)
0
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gb2019calculus1
0
votes
1
answer
6
GATEBOOK2019Calculus16
If $f'(x)=\frac{1}{3x^2}$ and $f(0)=1$ then the interval in which $f(1)$ lies is, $1 \leq f(1) \leq 2$ $3 \leq f(1) \leq 4$ $\frac{4}{3} \leq f(1) \leq \frac{3}{2}$ $\frac{2}{3} \leq f(1) \leq \frac{4}{3}$
asked
Dec 23, 2018
in
Calculus
by
Arjun
Veteran
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364k
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gb2019calculus1
0
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1
answer
7
GATEBOOK2019Calculus17
Maximum area of a rightangled triangle with hypotenuse $'h'$ is ____ $\frac{h^2}{2}$ $\frac{h^2}{3}$ $\frac{h^2}{4}$ $\frac{h^2}{5}$
asked
Dec 23, 2018
in
Calculus
by
Arjun
Veteran
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364k
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gb2019calculus1
0
votes
1
answer
8
GATEBOOK2019Calculus18
The integral $\int_{\infty}^{\infty} xe^{x^2} \: dx$ Converge to $'0'$ Converges to $'1'$ Diverges to $'\infty'$ Diverges to $' \infty'$
asked
Dec 23, 2018
in
Calculus
by
Arjun
Veteran
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364k
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gb2019calculus1
0
votes
1
answer
9
GATEBOOK2019Calculus19
The integral $\int_2^{\infty} \frac{dx}{\ell nx}$ Converges to $'0'$ Converges to $'1'$ Diverges Oscillates
asked
Dec 23, 2018
in
Calculus
by
Arjun
Veteran
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364k
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gb2019calculus1
0
votes
1
answer
10
GATEBOOK2019Calculus110
If $u(x,y) = \cos^{1} \bigg( \frac{x+y}{\sqrt{x}+ \sqrt{y}}, 0< x, y<1$ then $x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y} = $_____ $\cot u$ $\frac{1}{2} \cot u$ $\tan u$ $\frac{1}{2} \tan u$
asked
Dec 23, 2018
in
Calculus
by
Arjun
Veteran
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364k
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0
views
gb2019calculus1
0
votes
1
answer
11
GATEBOOK2019Calculus111
The value of $\int \int_R xy dx dy $ where $R$ is the region bounded by the $x$axis, the line $y=2x$ and the parabola $y=\frac{x^2}{4a}$ is _____ $\frac{4096}{5}a^3$ $\frac{4096}{7}a^4$ $\frac{2048}{3}a^3$ $\frac{2048}{3}a^4$
asked
Dec 23, 2018
in
Calculus
by
Arjun
Veteran
(
364k
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0
views
gb2019calculus1
0
votes
1
answer
12
GATEBOOK2019Calculus112
The cylinder $x^2 +z^2 =1$ is cut by the planes $y=0, z=0$ and $x=y$. The volume of the region in the 1st octant is _______
asked
Dec 23, 2018
in
Calculus
by
Arjun
Veteran
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364k
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gb2019calculus1
numericalanswers
0
votes
1
answer
13
GATEBOOK2019Calculus113
$\lim_{x \to 0} \frac{x \tan 2x  2x \tan x}{(1\cos2x)^2} = $_______ $2$ $2$ $\frac{1}{2}$ $\frac{1}{2}$
asked
Dec 23, 2018
in
Calculus
by
Arjun
Veteran
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364k
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0
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gb2019calculus1
0
votes
1
answer
14
GATEBOOK2019Calculus114
Let $f(x) = \begin{cases} 1x, & x<1 \\ (1x)(2x), & 1 \leq x \leq 2 \\ 3x, & x>2 \end{cases}$ then $f(x)$ is, not continuous at $x=1$ not differentiable at $x=1$ Differentiable at $x=2$ Not differentiable at $x=2$
asked
Dec 23, 2018
in
Calculus
by
Arjun
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364k
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0
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gb2019calculus1
0
votes
0
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15
GATEBOOK2019Calculus115
The values of $a, b, c$ ... $a=1, b=0, c=1$ $a=\frac{1}{2}, c=\frac{3}{2}, b \in R$ $a=\frac{3}{2}, c=\frac{1}{2}, b \in R$
asked
Dec 23, 2018
in
Calculus
by
Arjun
Veteran
(
364k
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0
views
gb2019calculus1
0
votes
1
answer
16
GATEBOOK2019Calculus116
Let $f(x) = \begin{cases} \frac{x^2}{2}, & 0 \leq x < 1 \\ 2x^23x+\frac{3}{2}, & 1 \leq x \leq 2 \end{cases}$ then which of the following is not correct? $f(x)$ is continuous for all $ x \in [0,2]$ $f'(x)$ is continuous for all $x \in [0,2]$ $f''(x)$ is continuous for all $x \in [0,2]$ None of these
asked
Dec 23, 2018
in
Calculus
by
Arjun
Veteran
(
364k
points)
1
view
gb2019calculus1
0
votes
1
answer
17
GATEBOOK2019Calculus117
The integral $\int_2^4 \frac{\log x^2}{\log x^2 + \log (3612x+x^2)} dx$ is equal to $2$ $4$ $1$ $6$
asked
Dec 23, 2018
in
Calculus
by
Arjun
Veteran
(
364k
points)
1
view
gb2019calculus1
0
votes
0
answers
18
GATEBOOK2019Calculus118
If $y=a \log x +bx^2 =x$ has its extremum values at $x=1$ and $x=2$ then $a=2, b=1$ $a=2, b=\frac{1}{2}$ $a=2, b=\frac{1}{2}$ $\text{None of the above}$
asked
Dec 23, 2018
in
Calculus
by
Arjun
Veteran
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364k
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0
views
gb2019calculus1
0
votes
1
answer
19
GATEBOOK2019Calculus119
$\lim_{x \to 0} \frac{\tan ^{1}x  \sin^{1}x}{x^3} =$____ $\infty$ $0$ $1$ $\frac{1}{2}$
asked
Dec 23, 2018
in
Calculus
by
Arjun
Veteran
(
364k
points)
2
views
gb2019calculus1
0
votes
1
answer
20
GATEBOOK2019Calculus120
The value of integral $\int_0^{2 \pi} \sin^2 x. \cos x^4 dx =$____ $0$ $\frac{\pi}{2}$ $\frac{\pi}{4}$ $\frac{\pi}{8}$
asked
Dec 23, 2018
in
Calculus
by
Arjun
Veteran
(
364k
points)
1
view
gb2019calculus1
0
votes
1
answer
21
Area between curves
The area between the parabola $x^2 = 8y$ and the straight line y= 8 is . I am getting $128√2$.
asked
Sep 3, 2018
in
Calculus
by
Jason
Active
(
1.5k
points)
6
views
engineeringmathematics
integration
0
votes
1
answer
22
lt x→0(3cosx+2sin3x)^(1/x)
asked
Aug 8, 2018
in
Calculus
by
Mani217
(
7
points)
19
views
+1
vote
1
answer
23
Finding Maxima Minima
The greatest value of the function f(x) = 2 sin x + sin 2x on the interval [ 0,3pi/2 ] is ____
asked
Jul 19, 2018
in
Calculus
by
srestha
Veteran
(
94k
points)
88
views
engineeringmathematics
maximaminima
calculus
0
votes
1
answer
24
CalculusSelf Doubt
Is the function $f(x)=\frac{1}{x^{\frac{1}{3}}}$ continous in the interval [1 0) ?
asked
Jul 17, 2018
in
Calculus
by
Ayush Upadhyaya
Boss
(
11.8k
points)
72
views
engineeringmathematics
calculus
continuity
0
votes
1
answer
25
ugc net 2018 july 82
Which of the following statements is false about convex minimization problem? If a local minimum exists, then it is a global minimum the set of all global minimum is a convex set the set of all global minimum is concave set for each is strictly convex function, if the function has minimum, then the minimum is a unique
asked
Jul 8, 2018
in
Calculus
by
pream sagar
(
385
points)
282
views
0
votes
2
answers
26
SELF DOUBT
0/infinity is determinent form or inderminent form while solving limits
asked
Jul 6, 2018
in
Calculus
by
eyeamgj
Active
(
4.1k
points)
64
views
0
votes
0
answers
27
ISI 2014 MMA  5
asked
Jun 12, 2018
in
Calculus
by
Sammohan Ganguly
(
435
points)
58
views
userisi2014
usermod
calculus
engineeringmathematics
0
votes
1
answer
28
ISI 2014 MMA 7
asked
Jun 12, 2018
in
Calculus
by
Sammohan Ganguly
(
435
points)
64
views
userisi2014
usermod
calculus
engineeringmathematics
0
votes
1
answer
29
Definite Integral
S = $\int_{0}^{2\Pi } \sqrt{4cos^{2}t +sin^{2}t} \, \, dt$ Please explain how to solve it.
asked
Jun 11, 2018
in
Calculus
by
ankitgupta.1729
Loyal
(
7.1k
points)
98
views
calculus
integration
engineeringmathematics
integrals
0
votes
1
answer
30
Calculus
asked
Jun 4, 2018
in
Calculus
by
mbisht
(
247
points)
60
views
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