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Recent questions and answers in Calculus
0
votes
1
answer
1
NIELIT 2016 MAR Scientist B  Section B: 14
The minimum value of $\mid x^25x+2\mid$ is $5$ $0$ $1$ $2$
answered
Jun 26
in
Calculus
by
Sherrinford03

39
views
nielit2016marscientistb
+1
vote
2
answers
2
ISI2019MMA24
Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a continuous function such that $\lim _{n\rightarrow \infty} f''(x)$ exists for every $x \in \mathbb{R}$, where $f''(x) = f \circ f^{n1}(x)$ for $n \geq 2$ ... $S \subset T$ $T \subset S$ $S = T$ None of the above
answered
Jun 11
in
Calculus
by
Amartya

463
views
isi2019mma
engineeringmathematics
calculus
limits
0
votes
1
answer
3
ISI2015MMA30
Suppose that a function $f$ defined on $\mathbb{R} ^2$ satisfies the following conditions: $\begin{array} &f(x+t,y) & = & f(x,y)+ty, \\ f(x,t+y) & = & f(x,y)+ tx \text{ and } \\ f(0,0) & = & K, \text{ a constant.} \end{array}$ Then for all $x,y \in \mathbb{R}, \:f(x,y)$ is equal to $K(x+y)$ $Kxy$ $K+xy$ none of the above
answered
May 29
in
Calculus
by
Amartya

69
views
isi2015mma
calculus
functions
nongate
0
votes
1
answer
4
NIELIT 2016 DEC Scientist B (CS)  Section B: 26
Consider the function $f(x)=\sin(x)$ in the interval $\bigg [\dfrac{ \pi}{4},7\dfrac{\pi}{4}\bigg ]$. The number and location(s) of the minima of this function are: One, at $\dfrac{\pi}{2} \\$ One, at $3\dfrac{\pi}{2} \\$ Two,at $\dfrac{\pi}{2}$ and $3\dfrac{\pi}{2} \\$ Two,at $\dfrac{\pi}{4}$ and$ 3\dfrac{\pi}{2}$
answered
May 25
in
Calculus
by
Mohit Kumar 6

40
views
nielit2016decscientistbcs
0
votes
1
answer
5
ISI2018MMA30
Consider the function $f(x)=\bigg(1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\dots+\frac{x^n}{n!}\bigg)e^{x}$, where $n\geq4$ is a positive integer. Which of the following statements is correct? $f$ has no local maximum For every $n$, $f$ has a local maximum at $x = 0$ ... at $x = 0$ when $n$ is even $f$ has no local extremum if $n$ is even and has a local maximum at $x = 0$ when $n$ is odd.
answered
May 24
in
Calculus
by
Amartya

152
views
isi2018mma
engineeringmathematics
calculus
maximaminima
0
votes
1
answer
6
ISI2018MMA29
Let $f$ be a continuous function with $f(1) = 1$. Define $F(t)=\int_{t}^{t^2}f(x)dx$. The value of $F’(1)$ is $2$ $1$ $1$ $2$
answered
May 24
in
Calculus
by
Amartya

178
views
isi2018mma
engineeringmathematics
calculus
integration
0
votes
2
answers
7
ISI2015MMA78
The value of $\displaystyle \lim_{n \to \infty} \left[ (n+1) \int_0^1 x^n \ln(1+x) dx \right]$ is $0$ $\ln 2$ $\ln 3$ $\infty$
answered
May 23
in
Calculus
by
Amartya

66
views
isi2015mma
calculus
limits
definiteintegrals
nongate
0
votes
1
answer
8
ISI2015MMA69
Consider the function $f(x) = \begin{cases} \int_0^x \{5+ \mid 1y \mid \} dy & \text{ if } x>2 \\ 5x+2 & \text{ if } x \leq 2 \end{cases}$ Then $f$ is not continuous at $x=2$ $f$ is continuous and differentiable everywhere $f$ is continuous everywhere but not differentiable at $x=1$ $f$ is continuous everywhere but not differentiable at $x=2$
answered
May 23
in
Calculus
by
Amartya

72
views
isi2015mma
calculus
continuity
differentiation
definiteintegrals
nongate
0
votes
1
answer
9
ISI2015MMA57
Suppose $a>0$. Consider the sequence $a_n = n \{ \sqrt[n]{ea} – \sqrt[n]{a}, \:\:\:\:\: n \geq 1$. Then $\underset{n \to \infty}{\lim} a_n$ does not exist $\underset{n \to \infty}{\lim} a_n=e$ $\underset{n \to \infty}{\lim} a_n=0$ none of the above
answered
May 22
in
Calculus
by
Amartya

59
views
isi2015mma
calculus
limits
+9
votes
5
answers
10
TIFR2014A9
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
May 8
in
Calculus
by
Joyoshish Saha

598
views
tifr2014
calculus
maximaminima
0
votes
1
answer
11
NIELIT 2016 MAR Scientist B  Section B: 13
$\underset{x\to 0}{\lim} \dfrac{(1\cos x)}{2}$ is equal to $0$ $1$ $1/3$ $1/2$
answered
Apr 1
in
Calculus
by
aman_0709

73
views
nielit2016marscientistb
0
votes
1
answer
12
NIELIT 2016 MAR Scientist B  Section B: 11
What is the derivative w.r.t $x$ of the function given by $\large \Phi(x)= \displaystyle \int_{0}^{x^2}\sqrt t\:dt$, $2x^2$ $\sqrt x$ $0$ $1$
answered
Apr 1
in
Calculus
by
haralk10

41
views
nielit2016marscientistb
0
votes
1
answer
13
NIELIT 2016 MAR Scientist B  Section B: 10
Maxima and minimum of the function $f(x)=2x^315x^2+36x+10$ occur; respectively at $x=3$ and $x=2$ $x=1$ and $x=3$ $x=2$ and $x=3$ $x=3$ and $x=4$
answered
Apr 1
in
Calculus
by
haralk10

46
views
nielit2016marscientistb
0
votes
1
answer
14
NIELIT 2016 MAR Scientist B  Section B: 9
The value of improper integral $\displaystyle\int_{0}^{1} x\ln x =?$ $1/4$ $0$ $1/4$ $1$
answered
Apr 1
in
Calculus
by
haralk10

46
views
nielit2016marscientistb
0
votes
0
answers
15
NIELIT 2016 MAR Scientist B  Section B: 8
If $\Delta f(x)= f(x+h)f(x)$, then a constant $k,\Delta k$ $1$ $0$ $f(k)f(0)$ $f(x+k)f(x)$
asked
Mar 31
in
Calculus
by
Lakshman Patel RJIT

49
views
nielit2016marscientistb
0
votes
1
answer
16
ISI2016DCG69
Consider the differential equation $(x^{2}y^{2})\frac{\mathrm{d} y}{\mathrm{d} x}=2xy.$ Assuming $y=10$ for $x=0,$ its solution is $x^{2}+(y5)^{2}=25$ $x^{2}+y^{2}=100$ $(x5)^{2}+y^{2}=125$ $(x5)^{2}+(y5)^{2}=50$
answered
Mar 15
in
Calculus
by
haralk10

42
views
isi2016dcg
calculus
differentialequation
nongate
0
votes
1
answer
17
ISI2016DCG68
The general solution of the differential equation $x+yx{y}'=0$ is (assuming $C$ as an arbitrary constant of integration) $y=x(\log x+C)$ $x=y(\log y+C)$ $y=x(\log y+C)$ $y=y(\log x+C)$
answered
Mar 14
in
Calculus
by
haralk10

41
views
isi2016dcg
calculus
differentialequation
nongate
0
votes
1
answer
18
ISI2016DCG67
The general solution of the differential equation $2y{y}'x=0$ is (assuming $C$ as an arbitrary constant of integration) $x^{2}y^{2}=C$ $2x^{2}y^{2}=C$ $2y^{2}x^{2}=C$ $x^{2}+y^{2}=C$
answered
Mar 14
in
Calculus
by
haralk10

46
views
isi2016dcg
calculus
differentialequation
nongate
0
votes
1
answer
19
ISI2015DCG50
The piecewise linear function for the following graph is $f(x) = \begin{cases} = x, \: x \leq 2 \\ =4, \: 2<x<3 \\ =x+1, \: x \geq 3 \end{cases}$ $f(x) = \begin{cases} = x2, \: x \leq 2 \\ =4, \: 2<x<3 \\ =x1, \: x \geq 3 \end{cases}$ ... $f(x) = \begin{cases} = 2x, \: x \leq 2 \\ =4, \: 2<x<3 \\ =x+1, \: x \geq 3 \end{cases}$
answered
Mar 14
in
Calculus
by
haralk10

42
views
isi2015dcg
calculus
functions
0
votes
1
answer
20
ISI2014DCG48
If $x$ is real, the set of real values of $a$ for which the function $y=x^2ax+12a^2$ is always greater than zero is $ \frac{2}{3} < a \leq \frac{2}{3}$ $ \frac{2}{3} \leq a < \frac{2}{3}$ $ \frac{2}{3} < a < \frac{2}{3}$ None of these
answered
Mar 13
in
Calculus
by
haralk10

36
views
isi2014dcg
calculus
functions
quadraticequations
0
votes
1
answer
21
TIFR2020A8
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
answered
Mar 1
in
Calculus
by
ankitgupta.1729

82
views
tifr2020
engineeringmathematics
calculus
maximaminima
0
votes
1
answer
22
TIFR2020A13
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
answered
Feb 19
in
Calculus
by
ankitgupta.1729

50
views
tifr2020
+2
votes
2
answers
23
ISI2014DCG6
If $f(x)$ is a real valued function such that $2f(x)+3f(x)=154x$, for every $x \in \mathbb{R}$, then $f(2)$ is $15$ $22$ $11$ $0$
answered
Jan 30
in
Calculus
by
Akumar20

139
views
isi2014dcg
calculus
functions
+1
vote
2
answers
24
MadeEasy Test Series: Calculus  Limits
How it solve this ?
answered
Jan 9
in
Calculus
by
Mayank Harbola

277
views
madeeasytestseries
calculus
limits
engineeringmathematics
+1
vote
2
answers
25
GATE199302.6
The value of the double integral $\int^{1}_{0} \int_{0}^{\frac{1}{x}} \frac {x}{1+y^2} dxdy$ is_________.
answered
Dec 31, 2019
in
Calculus
by
Verma Ashish

881
views
gate1993
calculus
integration
normal
+3
votes
5
answers
26
TIFR2019A15
Consider the matrix $A = \begin{bmatrix} \frac{1}{2} &\frac{1}{2} & 0\\ 0& \frac{3}{4} & \frac{1}{4}\\ 0& \frac{1}{4} & \frac{3}{4} \end{bmatrix}$ What is $\lim_{n→\infty}$A^n$ ? $\begin{bmatrix} \ 0 & 0 & 0\\ 0& 0 ... $\text{The limit exists, but it is none of the above}$
answered
Dec 5, 2019
in
Calculus
by
severustux

596
views
tifr2019
engineeringmathematics
calculus
limits
+22
votes
5
answers
27
GATE201436
If $\int \limits_0^{2 \pi} x \: \sin x dx=k\pi$, then the value of $k$ is equal to ______.
answered
Dec 1, 2019
in
Calculus
by
Lakshman Patel RJIT

3.7k
views
gate20143
calculus
integration
limits
numericalanswers
easy
+22
votes
4
answers
28
GATE2014347
The value of the integral given below is $\int \limits_0^{\pi} \: x^2 \: \cos x\:dx$ $2\pi$ $\pi$ $\pi$ $2\pi$
answered
Dec 1, 2019
in
Calculus
by
Lakshman Patel RJIT

2.5k
views
gate20143
calculus
limits
integration
normal
+6
votes
3
answers
29
ISRO201349
What is the least value of the function $f(x) = 2x^{2}8x3$ in the interval $[0, 5]$? $15$ $7$ $11$ $3$
answered
Nov 28, 2019
in
Calculus
by
Lakshman Patel RJIT

2.2k
views
isro2013
maximaminima
+1
vote
1
answer
30
TIFR2011MathsA19
The derivative of the function $\int_{0}^{\sqrt{x}} e^{t^{2}}dt$ at $x = 1$ is $e^{1}$ .
answered
Nov 25, 2019
in
Calculus
by
seetal samal

199
views
tifrmaths2011
calculus
differentiation
+1
vote
1
answer
31
TIFR2011MathsA21
Any continuous function from the open unit interval $(0, 1)$ to itself has a fixed point.
answered
Nov 25, 2019
in
Calculus
by
seetal samal

132
views
tifrmaths2011
continuity
+2
votes
2
answers
32
Integration
Solve the following $\int_{0}^{\infty}e^{x^2}x^4dx$
answered
Nov 22, 2019
in
Calculus
by
Lakshman Patel RJIT

240
views
engineeringmathematics
integration
calculus
+2
votes
1
answer
33
ISI2016MMA8
Let $g: \mathbb{R} \rightarrow \mathbb{R}$ be differentiable with $g'(x^2)=x^3$ for all $x>0$ and $g(1) =1$. Then $g(4)$ equals $64/5$ $32/5$ $37/5$ $67/5$
answered
Nov 19, 2019
in
Calculus
by
`JEET

88
views
isi2016mmamma
calculus
differentiation
+1
vote
3
answers
34
ISI2017DCG23
A determinant is chosen at random from the set of all determinants of order $2$ with elements $0$ or $1$ only. The probability of choosing a nonzero determinant is $\frac{3}{16}$ $\frac{3}{8}$ $\frac{1}{4}$ none of these
answered
Nov 19, 2019
in
Calculus
by
chirudeepnamini

89
views
isi2017dcg
probability
determinants
+41
votes
4
answers
35
GATE20129
Consider the function $f(x) = \sin(x)$ in the interval $x =\left[\frac{\pi}{4},\frac{7\pi}{4}\right]$. The number and location(s) of the local 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 $\dfrac{3\pi}{2}$
answered
Nov 13, 2019
in
Calculus
by
Obafgkme

5.2k
views
gate2012
calculus
maximaminima
normal
nielit
0
votes
1
answer
36
MadeEasy Workbook: Calculus  Maxima Minima
answered
Nov 1, 2019
in
Calculus
by
Kushagra गुप्ता

150
views
engineeringmathematics
calculus
maximaminima
madeeasybooklet
+2
votes
2
answers
37
ISI2015MMA10
The value of the infinite product $P=\frac{7}{9} \times \frac{26}{28} \times \frac{63}{65} \times \cdots \times \frac{n^31}{n^3+1} \times \cdots \text{ is }$ $1$ $2/3$ $7/3$ none of the above
answered
Oct 25, 2019
in
Calculus
by
techbd123

130
views
isi2015mma
calculus
limits
0
votes
1
answer
38
ISI2017DCG6
Let $f(x) = \dfrac{x1}{x+1}, \: f^{k+1}(x)=f\left(f^k(x)\right)$ for all $k=1, 2, 3, \dots , 99$. Then $f^{100}(10)$ is $1$ $10$ $100$ $101$
answered
Oct 21, 2019
in
Calculus
by
`JEET

73
views
isi2017dcg
calculus
functions
+1
vote
1
answer
39
ISI2015MMA36
For nonnegative integers $m$, $n$ define a function as follows $f(m,n) = \begin{cases} n+1 & \text{ if } m=0 \\ f(m1, 1) & \text{ if } m \neq 0, n=0 \\ f(m1, f(m,n1)) & \text{ if } m \neq 0, n \neq 0 \end{cases}$ Then the value of $f(1,1)$ is $4$ $3$ $2$ $1$
answered
Oct 19, 2019
in
Calculus
by
chirudeepnamini

64
views
isi2015mma
calculus
functions
nongate
+14
votes
3
answers
40
GATE19961.6
The formula used to compute an approximation for the second derivative of a function $f$ at a point $X_0$ is $\dfrac{f(x_0 +h) + f(x_0 – h)}{2}$ $\dfrac{f(x_0 +h)  f(x_0 – h)}{2h}$ $\dfrac{f(x_0 +h) + 2f(x_0) + f(x_0 – h)}{h^2}$ $\dfrac{f(x_0 +h)  2f(x_0) + f(x_0 – h)}{h^2}$
answered
Oct 18, 2019
in
Calculus
by
neeraj_bhatt

2k
views
gate1996
calculus
differentiation
normal
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