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Recent questions and answers in Calculus
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Recent questions and answers in Calculus
16
votes
6
answers
1
GATE2008-1
$\lim_{x \to \infty}\frac{x-\sin x}{x+\cos x}$ equals $1$ $-1$ $\infty$ $-\infty$
$\lim_{x \to \infty}\frac{x-\sin x}{x+\cos x}$ equals $1$ $-1$ $\infty$ $-\infty$
answered
5 days
ago
in
Calculus
Surya_Dev Chaturvedi
4.4k
views
gate2008
calculus
limits
easy
18
votes
4
answers
2
GATE2010-ME
The function $y=|2 - 3x|$ is continuous $∀ x ∈ R$ and differentiable $∀ x ∈ R$ is continuous $∀ x ∈ R$ and differentiable $∀ x ∈ R$ except at $x=\frac{3}{2}$ is continuous $∀ x ∈ R$ and differentiable $∀ x ∈ R$ except at $x=\frac{2}{3}$ is continuous $∀ x ∈ R$ except $x=3$ and differentiable $∀ x ∈ R$
The function $y=|2 - 3x|$ is continuous $∀ x ∈ R$ and differentiable $∀ x ∈ R$ is continuous $∀ x ∈ R$ and differentiable $∀ x ∈ R$ except at $x=\frac{3}{2}$ is continuous $∀ x ∈ R$ and differentiable $∀ x ∈ R$ except at $x=\frac{2}{3}$ is continuous $∀ x ∈ R$ except $x=3$ and differentiable $∀ x ∈ R$
answered
Dec 4, 2020
in
Calculus
StoneHeart
2.6k
views
calculus
gate2010me
engineering-mathematics
continuity
0
votes
1
answer
3
ISI2014-DCG-53
The value of the integral $\displaystyle{}\int_{-1}^1 \dfrac{x^2}{1+x^2} \sin x \sin 3x \sin 5x dx$ is $0$ $\frac{1}{2}$ $ – \frac{1}{2}$ $1$
The value of the integral $\displaystyle{}\int_{-1}^1 \dfrac{x^2}{1+x^2} \sin x \sin 3x \sin 5x dx$ is $0$ $\frac{1}{2}$ $ – \frac{1}{2}$ $1$
answered
Nov 14, 2020
in
Calculus
raja11sep
204
views
isi2014-dcg
calculus
integration
definite-integrals
12
votes
4
answers
4
GATE2005-IT-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 $\int_{0}^{2\pi}(x-\pi)^2 (\sin x) dx$ $-1$ $0$ $1$ $\pi$
answered
Oct 27, 2020
in
Calculus
jainanmol123
2.9k
views
gate2005-it
calculus
integration
normal
0
votes
1
answer
5
ISI2015-MMA-72
The map $f(x) = a_0 \cos \mid x \mid +a_1 \sin \mid x \mid +a_2 \mid x \mid ^3$ is differentiable at $x=0$ if and only if $a_1=0$ and $a_2=0$ $a_0=0$ and $a_1=0$ $a_1=0$ $a_0, a_1, a_2$ can take any real value
The map $f(x) = a_0 \cos \mid x \mid +a_1 \sin \mid x \mid +a_2 \mid x \mid ^3$ is differentiable at $x=0$ if and only if $a_1=0$ and $a_2=0$ $a_0=0$ and $a_1=0$ $a_1=0$ $a_0, a_1, a_2$ can take any real value
answered
Oct 15, 2020
in
Calculus
sparta
114
views
isi2015-mma
calculus
differentiation
53
votes
7
answers
6
GATE2014-1-47
A function $f(x)$ is continuous in the interval $[0,2]$. It is known that $f(0) = f(2) = -1$ and $f(1) = 1$. Which one of the following statements must be true? There exists a $y$ in the interval $(0,1)$ such that $f(y) = f(y+1)$ For every $y$ in the interval ... of the function in the interval $(0,2)$ is $1$ There exists a $y$ in the interval $(0,1)$ such that $f(y)$ = $-f(2-y)$
A function $f(x)$ is continuous in the interval $[0,2]$. It is known that $f(0) = f(2) = -1$ and $f(1) = 1$. Which one of the following statements must be true? There exists a $y$ in the interval $(0,1)$ such that $f(y) = f(y+1)$ For every $y$ ... maximum value of the function in the interval $(0,2)$ is $1$ There exists a $y$ in the interval $(0,1)$ such that $f(y)$ = $-f(2-y)$
answered
Oct 9, 2020
in
Calculus
prajjwalsingh_11
9.9k
views
gate2014-1
calculus
continuity
normal
9
votes
6
answers
7
TIFR2014-A-9
Solve min $x^{2}+y^{2}$ subject to $\begin {align*} x + y &\geq 10,\\ 2x + 3y &\geq 20,\\ x &\geq 4,\\ y &\geq 4. \end{align*}$ $32$ $50$ $52$ $100$ None of the above
Solve min $x^{2}+y^{2}$ subject to $\begin {align*} x + y &\geq 10,\\ 2x + 3y &\geq 20,\\ x &\geq 4,\\ y &\geq 4. \end{align*}$ $32$ $50$ $52$ $100$ None of the above
answered
Oct 2, 2020
in
Calculus
ankitgupta.1729
836
views
tifr2014
calculus
maxima-minima
3
votes
1
answer
8
ISI2014-DCG-31
For real $\alpha$, the value of $\int_{\alpha}^{\alpha+1} [x]dx$, where $[x]$ denotes the largest integer less than or equal to $x$, is $\alpha$ $[\alpha]$ $1$ $\dfrac{[\alpha] + [\alpha +1]}{2}$
For real $\alpha$, the value of $\int_{\alpha}^{\alpha+1} [x]dx$, where $[x]$ denotes the largest integer less than or equal to $x$, is $\alpha$ $[\alpha]$ $1$ $\dfrac{[\alpha] + [\alpha +1]}{2}$
answered
Sep 9, 2020
in
Calculus
neeraj_bhatt
144
views
isi2014-dcg
calculus
integration
definite-integrals
0
votes
0
answers
9
TIFR-2019-Maths-A: 6
The limit $\underset{n\rightarrow \infty }{\lim}\:n^{2}\int_{0}^{1}\:\frac{1}{\left ( 1+x^{2} \right )^{n}}\:dx$ is equal to $1$ $0$ $+\infty$ $1/2$
The limit $\underset{n\rightarrow \infty }{\lim}\:n^{2}\int_{0}^{1}\:\frac{1}{\left ( 1+x^{2} \right )^{n}}\:dx$ is equal to $1$ $0$ $+\infty$ $1/2$
asked
Aug 30, 2020
in
Calculus
soujanyareddy13
183
views
tifrmaths2019
limits
0
votes
0
answers
10
NIELIT 2017 OCT Scientific Assistant A (IT) - Section D: 6
A solution for the differential equation $x’(t) + 2x(t) = \delta(t)$ with initial condition $x(\overline{0}) = 0$ $e^{-2t}u(t)$ $e^{2t}u(t)$ $e^{-t}u(t)$ $e^{t}u(t)$
A solution for the differential equation $x’(t) + 2x(t) = \delta(t)$ with initial condition $x(\overline{0}) = 0$ $e^{-2t}u(t)$ $e^{2t}u(t)$ $e^{-t}u(t)$ $e^{t}u(t)$
asked
Aug 28, 2020
in
Calculus
Lakshman Patel RJIT
68
views
nielit2017oct-assistanta-it
differential-equation
non-gate
2
votes
2
answers
11
NIELIT 2016 MAR Scientist C - Section B: 2
The function $f(x)=x^{5}-5x^{4}+5x^{3}-1$ has one minima and two maxima two minima and one maxima two minima and two maxima one minima and one maxima
The function $f(x)=x^{5}-5x^{4}+5x^{3}-1$ has one minima and two maxima two minima and one maxima two minima and two maxima one minima and one maxima
asked
Apr 2, 2020
in
Calculus
Lakshman Patel RJIT
120
views
nielit2016mar-scientistc
calculus
0
votes
1
answer
12
NIELIT 2016 MAR Scientist C - Section B: 10
$\underset{x \rightarrow 0}{\lim} \dfrac{x^{3}+x^{2}-5x-2}{2x^{3}-7x^{2}+4x+4}=?$ $-0.5$ $(0.5)$ $\infty$ None of the above
$\underset{x \rightarrow 0}{\lim} \dfrac{x^{3}+x^{2}-5x-2}{2x^{3}-7x^{2}+4x+4}=?$ $-0.5$ $(0.5)$ $\infty$ None of the above
asked
Apr 2, 2020
in
Calculus
Lakshman Patel RJIT
81
views
nielit2016mar-scientistc
engineering-mathematics
calculus
0
votes
1
answer
13
NIELIT 2016 MAR Scientist C - Section B: 11
$\displaystyle \int_{0}^{\dfrac{\pi}{2}} \sin^{7}\theta \cos ^{4} \theta d\theta=?$ $16/1155$ $16/385$ $16\pi/385$ $8\pi/385$
$\displaystyle \int_{0}^{\dfrac{\pi}{2}} \sin^{7}\theta \cos ^{4} \theta d\theta=?$ $16/1155$ $16/385$ $16\pi/385$ $8\pi/385$
asked
Apr 2, 2020
in
Calculus
Lakshman Patel RJIT
61
views
nielit2016mar-scientistc
engineering-mathematics
calculus
0
votes
0
answers
14
NIELIT 2016 MAR Scientist C - Section B: 12
$\displaystyle \lim_{x \rightarrow a}\frac{1}{x^{2}-a^{2}} \displaystyle \int_{a}^{x}\sin (t^{2})dt=$? $2a \sin (a^{2})$ $2a$ $\sin (a^{2})$ None of the above
$\displaystyle \lim_{x \rightarrow a}\frac{1}{x^{2}-a^{2}} \displaystyle \int_{a}^{x}\sin (t^{2})dt=$? $2a \sin (a^{2})$ $2a$ $\sin (a^{2})$ None of the above
asked
Apr 2, 2020
in
Calculus
Lakshman Patel RJIT
45
views
nielit2016mar-scientistc
engineering-mathematics
calculus
0
votes
1
answer
15
NIELIT 2016 MAR Scientist C - Section B: 13
$\displaystyle \lim_{x \rightarrow 0}\frac{1}{x^{6}} \displaystyle \int_{0}^{x^{2}}\frac{t^{2}dt}{t^{6}+1}=$? $1/4$ $1/3$ $1/2$ $1$
$\displaystyle \lim_{x \rightarrow 0}\frac{1}{x^{6}} \displaystyle \int_{0}^{x^{2}}\frac{t^{2}dt}{t^{6}+1}=$? $1/4$ $1/3$ $1/2$ $1$
asked
Apr 2, 2020
in
Calculus
Lakshman Patel RJIT
68
views
nielit2016mar-scientistc
calculus
0
votes
1
answer
16
NIELIT 2016 MAR Scientist C - Section B: 17
A ladder $13$ feet long rests against the side of a house. The bottom of the ladder slides away from the house at a rate of $0.5$ ft/s. How fast is the top of the ladder sliding down the wall when the bottom of the ladder is $5$ ... $-\dfrac{5}{24} \text {ft/s} \\$ $-\dfrac{5}{12} \text{ ft/s}$
A ladder $13$ feet long rests against the side of a house. The bottom of the ladder slides away from the house at a rate of $0.5$ ft/s. How fast is the top of the ladder sliding down the wall when the bottom of the ladder is $5$ feet from the house? $\dfrac{5}{24} \text{ ft/s} \\$ $\dfrac{5}{12} \text{ ft/s} \\$ $-\dfrac{5}{24} \text {ft/s} \\$ $-\dfrac{5}{12} \text{ ft/s}$
asked
Apr 2, 2020
in
Calculus
Lakshman Patel RJIT
72
views
nielit2016mar-scientistc
engineering-mathematics
calculus
0
votes
1
answer
17
NIELIT 2017 OCT Scientific Assistant A (CS) - Section B: 18
What is the maximum value of the function $f(x) = 2x^{2} – 2x + 6$ in the interval $[0,2]?$ $6$ $10$ $12$ $5,5$
What is the maximum value of the function $f(x) = 2x^{2} – 2x + 6$ in the interval $[0,2]?$ $6$ $10$ $12$ $5,5$
asked
Apr 1, 2020
in
Calculus
Lakshman Patel RJIT
112
views
nielit2017oct-assistanta-cs
engineering-mathematics
calculus
maxima-minima
0
votes
1
answer
18
NIELIT 2017 OCT Scientific Assistant A (CS) - Section B: 19
The value of the Integral $I = \displaystyle{}\int_{0}^{\pi/2} x^{2}\sin x dx$ is $(x+2)/2$ $2/(\pi-2)$ $\pi – 2$ $\pi + 2$
The value of the Integral $I = \displaystyle{}\int_{0}^{\pi/2} x^{2}\sin x dx$ is $(x+2)/2$ $2/(\pi-2)$ $\pi – 2$ $\pi + 2$
asked
Apr 1, 2020
in
Calculus
Lakshman Patel RJIT
91
views
nielit2017oct-assistanta-cs
engineering-mathematics
calculus
definite-integrals
0
votes
1
answer
19
NIELIT 2017 DEC Scientific Assistant A - Section B: 10
The function $f\left ( x \right )=\dfrac{x^{2}-1}{x-1}$ at $x=1$ is : Continuous and differentiable Continuous but not differentiable Differentiable but not continuous Neither continuous nor differentiable
The function $f\left ( x \right )=\dfrac{x^{2}-1}{x-1}$ at $x=1$ is : Continuous and differentiable Continuous but not differentiable Differentiable but not continuous Neither continuous nor differentiable
asked
Mar 31, 2020
in
Calculus
Lakshman Patel RJIT
235
views
nielit2017dec-assistanta
engineering-mathematics
calculus
continuity
0
votes
1
answer
20
NIELIT 2016 MAR Scientist B - Section B: 5
The greatest and the least value of $f(x)=x^4-8x^3+22x^2-24x+1$ in $[0,2]$ are $0,8$ $0,-8$ $1,8$ $1,-8$
The greatest and the least value of $f(x)=x^4-8x^3+22x^2-24x+1$ in $[0,2]$ are $0,8$ $0,-8$ $1,8$ $1,-8$
asked
Mar 31, 2020
in
Calculus
Lakshman Patel RJIT
100
views
nielit2016mar-scientistb
engineering-mathematics
calculus
maxima-minima
0
votes
1
answer
21
NIELIT 2016 MAR Scientist B - Section B: 9
The value of improper integral $\displaystyle\int_{0}^{1} x\ln x =?$ $1/4$ $0$ $-1/4$ $1$
The value of improper integral $\displaystyle\int_{0}^{1} x\ln x =?$ $1/4$ $0$ $-1/4$ $1$
asked
Mar 31, 2020
in
Calculus
Lakshman Patel RJIT
124
views
nielit2016mar-scientistb
engineering-mathematics
calculus
integration
definite-integrals
0
votes
1
answer
22
NIELIT 2016 MAR Scientist B - Section B: 10
Maxima and minimum of the function $f(x)=2x^3-15x^2+36x+10$ occur; respectively at $x=3$ and $x=2$ $x=1$ and $x=3$ $x=2$ and $x=3$ $x=3$ and $x=4$
Maxima and minimum of the function $f(x)=2x^3-15x^2+36x+10$ occur; respectively at $x=3$ and $x=2$ $x=1$ and $x=3$ $x=2$ and $x=3$ $x=3$ and $x=4$
asked
Mar 31, 2020
in
Calculus
Lakshman Patel RJIT
105
views
nielit2016mar-scientistb
engineering-mathematics
calculus
maxima-minima
0
votes
1
answer
23
NIELIT 2016 MAR Scientist B - Section B: 11
What is the derivative w.r.t $x$ of the function given by $\large \Phi(x)= \displaystyle \int_{0}^{x^2}\sqrt t\:dt$, $2x^2$ $\sqrt x$ $0$ $1$
What is the derivative w.r.t $x$ of the function given by $\large \Phi(x)= \displaystyle \int_{0}^{x^2}\sqrt t\:dt$, $2x^2$ $\sqrt x$ $0$ $1$
asked
Mar 31, 2020
in
Calculus
Lakshman Patel RJIT
112
views
nielit2016mar-scientistb
engineering-mathematics
calculus
integration
definite-integrals
0
votes
1
answer
24
NIELIT 2016 MAR Scientist B - Section B: 13
$\underset{x\to 0}{\lim} \dfrac{(1-\cos x)}{2}$ is equal to $0$ $1$ $1/3$ $1/2$
$\underset{x\to 0}{\lim} \dfrac{(1-\cos x)}{2}$ is equal to $0$ $1$ $1/3$ $1/2$
asked
Mar 31, 2020
in
Calculus
Lakshman Patel RJIT
147
views
nielit2016mar-scientistb
engineering-mathematics
calculus
limits
0
votes
1
answer
25
NIELIT 2016 MAR Scientist B - Section B: 14
The minimum value of $\mid x^2-5x+2\mid$ is $-5$ $0$ $-1$ $-2$
The minimum value of $\mid x^2-5x+2\mid$ is $-5$ $0$ $-1$ $-2$
asked
Mar 31, 2020
in
Calculus
Lakshman Patel RJIT
114
views
nielit2016mar-scientistb
engineering-mathematics
calculus
maxima-minima
0
votes
0
answers
26
NIELIT 2016 MAR Scientist B - Section B: 15
Differential equation, $\dfrac{d^2x}{dt^2}+10\dfrac{dx}{dt}+25x=0$ will have a solution of the form $(C_1+C_2t)e^{-5t}$ $C_1e^{-2t}$ $C_1e^{-5t}+C_2e^{5t}$ $C_1e^{-5t}+C_2e^{2t}$ where $C_1$ and $C_2$ are constants.
Differential equation, $\dfrac{d^2x}{dt^2}+10\dfrac{dx}{dt}+25x=0$ will have a solution of the form $(C_1+C_2t)e^{-5t}$ $C_1e^{-2t}$ $C_1e^{-5t}+C_2e^{5t}$ $C_1e^{-5t}+C_2e^{2t}$ where $C_1$ and $C_2$ are constants.
asked
Mar 31, 2020
in
Calculus
Lakshman Patel RJIT
69
views
nielit2016mar-scientistb
non-gate
differential-equation
0
votes
1
answer
27
NIELIT 2016 DEC Scientist B (CS) - Section B: 26
Consider the function $f(x)=\sin(x)$ in the interval $\bigg [\dfrac{ \pi}{4},\dfrac{7\pi}{4}\bigg ]$. The number and location(s) of the minima of this function are: One, at $\dfrac{\pi}{2} \\$ One, at $\dfrac{3\pi}{2} \\$ Two, at $\dfrac{\pi}{2}$ and $\dfrac{3\pi}{2} \\$ Two, at $\dfrac{\pi}{4}$ and $\dfrac{3\pi}{2}$
Consider the function $f(x)=\sin(x)$ in the interval $\bigg [\dfrac{ \pi}{4},\dfrac{7\pi}{4}\bigg ]$. The number and location(s) of the minima of this function are: One, at $\dfrac{\pi}{2} \\$ One, at $\dfrac{3\pi}{2} \\$ Two, at $\dfrac{\pi}{2}$ and $\dfrac{3\pi}{2} \\$ Two, at $\dfrac{\pi}{4}$ and $\dfrac{3\pi}{2}$
asked
Mar 31, 2020
in
Calculus
Lakshman Patel RJIT
126
views
nielit2016dec-scientistb-cs
engineering-mathematics
calculus
maxima-minima
0
votes
1
answer
28
TIFR2020-A-13
What is the area of the largest rectangle that can be inscribed in a circle of radius $R$? $R^{2}/2$ $\pi \times R^{2}/2$ $R^{2}$ $2R^{2}$ None of the above
What is the area of the largest rectangle that can be inscribed in a circle of radius $R$? $R^{2}/2$ $\pi \times R^{2}/2$ $R^{2}$ $2R^{2}$ None of the above
asked
Feb 11, 2020
in
Calculus
Lakshman Patel RJIT
90
views
tifr2020
0
votes
1
answer
29
TIFR2020-A-8
Consider a function $f:[0,1]\rightarrow [0,1]$ which is twice differentiable in $(0,1).$ Suppose it has exactly one global maximum and exactly one global minimum inside $(0,1)$. What can you say about the behaviour of the first derivative $f'$ ... is zero at at least one point $f'$ is zero at at least two points, $f''$ is zero at at least two points
Consider a function $f:[0,1]\rightarrow [0,1]$ which is twice differentiable in $(0,1).$ Suppose it has exactly one global maximum and exactly one global minimum inside $(0,1)$. What can you say about the behaviour of the first derivative $f'$ and and second derivative $f''$ ... $f'$ is zero at at least two points, $f''$ is zero at at least two points
asked
Feb 10, 2020
in
Calculus
Lakshman Patel RJIT
178
views
tifr2020
engineering-mathematics
calculus
maxima-minima
2
votes
1
answer
30
ISI2014-DCG-2
Let $a_n=\bigg( 1 – \frac{1}{\sqrt{2}} \bigg) \cdots \bigg( 1 – \frac{1}{\sqrt{n+1}} \bigg), \: n \geq 1$. Then $\underset{n \to \infty}{\lim} a_n$ equals $1$ does not exist equals $\frac{1}{\sqrt{\pi}}$ equals $0$
Let $a_n=\bigg( 1 – \frac{1}{\sqrt{2}} \bigg) \cdots \bigg( 1 – \frac{1}{\sqrt{n+1}} \bigg), \: n \geq 1$. Then $\underset{n \to \infty}{\lim} a_n$ equals $1$ does not exist equals $\frac{1}{\sqrt{\pi}}$ equals $0$
asked
Sep 23, 2019
in
Calculus
Arjun
278
views
isi2014-dcg
calculus
limits
4
votes
4
answers
31
ISI2014-DCG-3
$\underset{x \to \infty}{\lim} \left( \frac{3x-1}{3x+1} \right) ^{4x}$ equals $1$ $0$ $e^{-8/3}$ $e^{4/9}$
$\underset{x \to \infty}{\lim} \left( \frac{3x-1}{3x+1} \right) ^{4x}$ equals $1$ $0$ $e^{-8/3}$ $e^{4/9}$
asked
Sep 23, 2019
in
Calculus
Arjun
427
views
isi2014-dcg
calculus
limits
3
votes
2
answers
32
ISI2014-DCG-4
$\underset{n \to \infty}{\lim} \dfrac{1}{n} \bigg( \dfrac{n}{n+1} + \dfrac{n}{n+2} + \cdots + \dfrac{n}{2n} \bigg)$ is equal to $\infty$ $0$ $\log_e 2$ $1$
$\underset{n \to \infty}{\lim} \dfrac{1}{n} \bigg( \dfrac{n}{n+1} + \dfrac{n}{n+2} + \cdots + \dfrac{n}{2n} \bigg)$ is equal to $\infty$ $0$ $\log_e 2$ $1$
asked
Sep 23, 2019
in
Calculus
Arjun
304
views
isi2014-dcg
calculus
limits
2
votes
2
answers
33
ISI2014-DCG-6
If $f(x)$ is a real valued function such that $2f(x)+3f(-x)=15-4x$, for every $x \in \mathbb{R}$, then $f(2)$ is $-15$ $22$ $11$ $0$
If $f(x)$ is a real valued function such that $2f(x)+3f(-x)=15-4x$, for every $x \in \mathbb{R}$, then $f(2)$ is $-15$ $22$ $11$ $0$
asked
Sep 23, 2019
in
Calculus
Arjun
201
views
isi2014-dcg
calculus
functions
2
votes
3
answers
34
ISI2014-DCG-7
If $f(x) = \dfrac{\sqrt{3} \sin x}{2+\cos x}$, then the range of $f(x)$ is the interval $[-1 , \sqrt{3}{/2}]$ the interval $[-\sqrt{3}{/2}, 1]$ the interval $[-1, 1]$ none of these
If $f(x) = \dfrac{\sqrt{3} \sin x}{2+\cos x}$, then the range of $f(x)$ is the interval $[-1 , \sqrt{3}{/2}]$ the interval $[-\sqrt{3}{/2}, 1]$ the interval $[-1, 1]$ none of these
asked
Sep 23, 2019
in
Calculus
Arjun
147
views
isi2014-dcg
calculus
functions
range
2
votes
1
answer
35
ISI2014-DCG-12
The integral $\int _0^{\frac{\pi}{2}} \frac{\sin^{50} x}{\sin^{50}x +\cos^{50}x} dx$ equals $\frac{3 \pi}{4}$ $\frac{\pi}{3}$ $\frac{\pi}{4}$ none of these
The integral $\int _0^{\frac{\pi}{2}} \frac{\sin^{50} x}{\sin^{50}x +\cos^{50}x} dx$ equals $\frac{3 \pi}{4}$ $\frac{\pi}{3}$ $\frac{\pi}{4}$ none of these
asked
Sep 23, 2019
in
Calculus
Arjun
220
views
isi2014-dcg
calculus
definite-integrals
integration
2
votes
1
answer
36
ISI2014-DCG-13
Let the function $f(x)$ be defined as $f(x)=\mid x-1 \mid + \mid x-2 \:\mid$. Then which of the following statements is true? $f(x)$ is differentiable at $x=1$ $f(x)$ is differentiable at $x=2$ $f(x)$ is differentiable at $x=1$ but not at $x=2$ none of the above
Let the function $f(x)$ be defined as $f(x)=\mid x-1 \mid + \mid x-2 \:\mid$. Then which of the following statements is true? $f(x)$ is differentiable at $x=1$ $f(x)$ is differentiable at $x=2$ $f(x)$ is differentiable at $x=1$ but not at $x=2$ none of the above
asked
Sep 23, 2019
in
Calculus
Arjun
170
views
isi2014-dcg
calculus
differentiation
2
votes
2
answers
37
ISI2014-DCG-17
$\underset{x \to 2}{\lim} \dfrac{1}{1+e^{\frac{1}{x-2}}}$ is $0$ $1/2$ $1$ non-existent
$\underset{x \to 2}{\lim} \dfrac{1}{1+e^{\frac{1}{x-2}}}$ is $0$ $1/2$ $1$ non-existent
asked
Sep 23, 2019
in
Calculus
Arjun
163
views
isi2014-dcg
calculus
limits
3
votes
1
answer
38
ISI2014-DCG-19
It is given that $e^a+e^b=10$ where $a$ and $b$ are real. Then the maximum value of $(e^a+e^b+e^{a+b}+1)$ is $36$ $\infty$ $25$ $21$
It is given that $e^a+e^b=10$ where $a$ and $b$ are real. Then the maximum value of $(e^a+e^b+e^{a+b}+1)$ is $36$ $\infty$ $25$ $21$
asked
Sep 23, 2019
in
Calculus
Arjun
139
views
isi2014-dcg
calculus
maxima-minima
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