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Limits,
Continuity,
and
Differentiability,
Maxima and minima,
Mean value theorem,
Integration.
Recent questions in Calculus
0
votes
0
answers
1
GATEBOOK-2019-Calculus1-1
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
Veteran
(
364k
points)
3
views
gb2019-calculus1
numerical-answers
0
votes
1
answer
2
GATEBOOK-2019-Calculus1-2
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
(
364k
points)
0
views
gb2019-calculus1
0
votes
1
answer
3
GATEBOOK-2019-Calculus1-3
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
Veteran
(
364k
points)
3
views
gb2019-calculus1
0
votes
1
answer
4
GATEBOOK-2019-Calculus1-4
The value of integral $\int_1^3 \frac{\mid x-2 \mid}{x} \: dx$ is ____
asked
Dec 23, 2018
in
Calculus
by
Arjun
Veteran
(
364k
points)
5
views
gb2019-calculus1
numerical-answers
0
votes
1
answer
5
GATEBOOK-2019-Calculus1-5
$\lim_{n \rightarrow \infty} (2n^4)^{\frac{1}{3n}} =$ $e$ $1$ $2^{\frac{1}{3}}$ $0$
asked
Dec 23, 2018
in
Calculus
by
Arjun
Veteran
(
364k
points)
0
views
gb2019-calculus1
0
votes
1
answer
6
GATEBOOK-2019-Calculus1-6
If $f'(x)=\frac{1}{3-x^2}$ 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
(
364k
points)
0
views
gb2019-calculus1
0
votes
1
answer
7
GATEBOOK-2019-Calculus1-7
Maximum area of a right-angled 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
(
364k
points)
0
views
gb2019-calculus1
0
votes
1
answer
8
GATEBOOK-2019-Calculus1-8
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
(
364k
points)
0
views
gb2019-calculus1
0
votes
1
answer
9
GATEBOOK-2019-Calculus1-9
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
(
364k
points)
0
views
gb2019-calculus1
0
votes
1
answer
10
GATEBOOK-2019-Calculus1-10
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
(
364k
points)
0
views
gb2019-calculus1
0
votes
1
answer
11
GATEBOOK-2019-Calculus1-11
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
points)
0
views
gb2019-calculus1
0
votes
1
answer
12
GATEBOOK-2019-Calculus1-12
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 1-st octant is _______
asked
Dec 23, 2018
in
Calculus
by
Arjun
Veteran
(
364k
points)
0
views
gb2019-calculus1
numerical-answers
0
votes
1
answer
13
GATEBOOK-2019-Calculus1-13
$\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
(
364k
points)
0
views
gb2019-calculus1
0
votes
1
answer
14
GATEBOOK-2019-Calculus1-14
Let $f(x) = \begin{cases} 1-x, & x<1 \\ (1-x)(2-x), & 1 \leq x \leq 2 \\ 3-x, & x>2 \end{cases}$ 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
Veteran
(
364k
points)
0
views
gb2019-calculus1
0
votes
0
answers
15
GATEBOOK-2019-Calculus1-15
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
points)
0
views
gb2019-calculus1
0
votes
1
answer
16
GATEBOOK-2019-Calculus1-16
Let $f(x) = \begin{cases} \frac{x^2}{2}, & 0 \leq x < 1 \\ 2x^2-3x+\frac{3}{2}, & 1 \leq x \leq 2 \end{cases}$ 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)
12
views
gb2019-calculus1
0
votes
1
answer
17
GATEBOOK-2019-Calculus1-17
The integral $\int_2^4 \frac{\log x^2}{\log x^2 + \log (36-12x+x^2)} dx$ is equal to $2$ $4$ $1$ $6$
asked
Dec 23, 2018
in
Calculus
by
Arjun
Veteran
(
364k
points)
9
views
gb2019-calculus1
0
votes
0
answers
18
GATEBOOK-2019-Calculus1-18
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
(
364k
points)
0
views
gb2019-calculus1
0
votes
1
answer
19
GATEBOOK-2019-Calculus1-19
$\lim_{x \to 0} \frac{\tan ^{-1}x - \sin^{-1}x}{x^3} =$____ $\infty$ $0$ $1$ $-\frac{1}{2}$
asked
Dec 23, 2018
in
Calculus
by
Arjun
Veteran
(
364k
points)
3
views
gb2019-calculus1
0
votes
1
answer
20
GATEBOOK-2019-Calculus1-20
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
gb2019-calculus1
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
engineering-mathematics
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
engineering-mathematics
maxima-minima
calculus
0
votes
1
answer
24
Calculus-Self 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
engineering-mathematics
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
engineering-mathematics
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
engineering-mathematics
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)
99
views
calculus
integration
engineering-mathematics
integrals
0
votes
1
answer
30
Calculus
asked
Jun 4, 2018
in
Calculus
by
mbisht
(
247
points)
61
views
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