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1
ISI2018MMA28
Consider the following functions $f(x)=\left\{\begin{matrix} 1 &, if\ x \leq 1 \\ 0 & ,if\ x>1 \end{matrix}\right.$ ... at $ 1$ $h_2$ is continuous everywhere and $h_1$ has discontinuity at $ 2$ $h_1$ has discontinuity at $ 2$ and $h_2$ has discontinuity at $ 1$.
asked
May 11
in
Calculus
by
akash.dinkar12
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isi2018
engineeringmathematics
calculus
continuity
0
votes
0
answers
2
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.
asked
May 11
in
Calculus
by
akash.dinkar12
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(
40.5k
points)

76
views
isi2018
engineeringmathematics
calculus
maximaminima
0
votes
0
answers
3
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 $2$ $1$ $1$ $2$
asked
May 11
in
Calculus
by
akash.dinkar12
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(
40.5k
points)

33
views
isi2018
engineeringmathematics
calculus
integration
0
votes
1
answer
4
ISI2018MMA19
Let $X_1,X_2, . . . ,X_n$ be independent and identically distributed with $P(X_i = 1) = P(X_i = −1) = p\ $and$ P(X_i = 0) = 1 − 2p$ for all $i = 1, 2, . . . , n.$ ... $a_n \rightarrow p, b_n \rightarrow p,c_n \rightarrow 12p$ $a_n \rightarrow1/2, b_n \rightarrow1/2,c_n \rightarrow0$ $a_n \rightarrow0, b_n \rightarrow0,c_n \rightarrow1$
asked
May 11
in
Calculus
by
akash.dinkar12
Boss
(
40.5k
points)

23
views
isi2018
engineeringmathematics
calculus
limits
0
votes
1
answer
5
ISI2019MMA30
Consider the function $h$ defined on $\{0,1,…….10\}$ with $h(0)=0, \: h(10)=10 $ and $2[h(i)h(i1)] = h(i+1) – h(i) \: \text{ for } i = 1,2, \dots ,9.$ Then the value of $h(1)$ is $\frac{1}{2^91}\\$ $\frac{10}{2^9+1}\\$ $\frac{10}{2^{10}1}\\$ $\frac{1}{2^{10}+1}$
asked
May 7
in
Calculus
by
Sayan Bose
Loyal
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6.9k
points)

316
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isi2019
engineeringmathematics
discretemathematics
settheory&algebra
functions
0
votes
1
answer
6
ISI2019MMA29
Let $\psi : \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function with $\psi(y) =0$ for all $y \notin [0,1]$ and $\int_{0}^{1} \psi(y) dy=1$. Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a twice differentiable function. Then the value of $\lim _{n\rightarrow \infty}n \int_{0}^{100} f(x)\psi(nx)dx$ is $f(0)$ $f’(0)$ $f’’(0)$ $f(100)$
asked
May 7
in
Calculus
by
Sayan Bose
Loyal
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6.9k
points)

347
views
isi2019
engineeringmathematics
calculus
integration
0
votes
1
answer
7
ISI2019MMA28
Consider the functions $f,g:[0,1] \rightarrow [0,1]$ given by $f(x)=\frac{1}{2}x(x+1) \text{ and } g(x)=\frac{1}{2}x^2(x+1).$ Then the area enclosed between the graphs of $f^{1}$ and $g^{1}$ is $1/4$ $1/6$ $1/8$ $1/24$
asked
May 7
in
Calculus
by
Sayan Bose
Loyal
(
6.9k
points)

617
views
isi2019
calculus
engineeringmathematics
0
votes
1
answer
8
ISI2019MMA25
Let $a,b,c$ be nonzero real numbers such that $\int_{0}^{1} (1 + \cos^8x)(ax^2 + bx +c)dx = \int_{0}^{2}(1+ \cos^8x)(ax^2 + bx + c) dx =0$ Then the quadratic equation $ax^2 + bx +c=0$ has no roots in $(0,2)$ one root in $(0,2)$ and one root outside this interval one repeated root in $(0,2)$ two distinct real roots in $(0,2)$
asked
May 7
in
Calculus
by
Sayan Bose
Loyal
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6.9k
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204
views
isi2019
engineeringmathematics
calculus
integration
+1
vote
1
answer
9
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
asked
May 7
in
Calculus
by
Sayan Bose
Loyal
(
6.9k
points)

214
views
isi2019
engineeringmathematics
calculus
limits
0
votes
1
answer
10
ISI2019MMA21
A function $f:\mathbb{R^2} \rightarrow \mathbb{R}$ is called degenerate on $x_i$, if $f(x_1,x_2)$ remains constant when $x_i$ varies $(i=1,2)$. Define $f(x_1,x_2) = \mid 2^{\pi _i/x_1} \mid ^{x_2} \text{ for } x_1 \neq 0$, where $i = \sqrt {1}$. ... $x_1$ but not on $x_2$ $f$ is degenerate on $x_2$ but not on $x_1$ $f$ is neither degenerate on $x_1$ nor on $x_2$
asked
May 7
in
Calculus
by
Sayan Bose
Loyal
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6.9k
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373
views
isi2019
engineeringmathematics
calculus
0
votes
1
answer
11
ISI2019MMA5
If $f(a)=2, \: f’(a) = 1, \: g(a) =1$ and $g’(a) =2$, then the value of $\lim _{x\rightarrow a}\frac{g(x) f(a) – f(x) g(a)}{xa}$ is $5$ $3$ $3$ $5$
asked
May 6
in
Calculus
by
Sayan Bose
Loyal
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6.9k
points)

138
views
isi2019
calculus
limits
0
votes
0
answers
12
Gate 2002  ME
Which of the following functions is not differentiable in the domain $[1,1]$ ? (a) $f(x) = x^2$ (b) $f(x) = x1$ (c) $f(x) = 2$ (d) $f(x) = Maximum (x,x)$
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May 4
in
Calculus
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balchandar reddy san
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46
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engineeringmathematics
usergate2002
usermod
calculus
differentiability
+1
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1
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13
ISIMMA 2019 Sample Questions23
For $n \geq1$, Let $a_{n} = \frac{1}{2^{2}} + \frac{2}{3^{2}} +.....+ \frac{n}{(n+1)^{2}}$ and $b_{n} = c_{0} + c_{1}r + c_{2}r^{2}+.....+c_{n}r^{n},$ where$c_{k} \leq M$ for all integers $k$ ... not a Cauchy sequence (C) $\{a_n\}$ is not a Cauchy sequence but $\{b_n\}$ is a Cauchy sequence (D) neither $\{a_n\}$ nor $\{b_n\}$ is a Cauchy sequence.
asked
Mar 17
in
Calculus
by
ankitgupta.1729
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11.3k
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97
views
sequenceseries
calculus
0
votes
1
answer
14
ISI MMA2015
Let, $a_{n} \;=\; \left ( 1\frac{1}{\sqrt{2}} \right ) ... \left ( 1 \frac{1}{\sqrt{n+1}} \right )$ , $n \geq 1$. Then $\lim_{n\rightarrow \infty } a_{n}$ (A) equals $1$ (B) does not exist (C) equals $\frac{1}{\sqrt{\pi }}$ (D) equals $0$
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Feb 21
in
Calculus
by
ankitgupta.1729
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11.3k
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128
views
engineeringmathematics
calculus
userisi2015
usermod
sequenceseries
limits
+1
vote
1
answer
15
ISI MMA2015
If two real polynomials $f(x)$ and $g(x)$ of degrees $m\;(\geq2)$ and $n\;(\geq1)$ respectively, satisfy $f(x^{2}+1) = f(x)g(x)$ $,$ for every $x\in \mathbb{R}$ , then (A) $f$ has exactly one real root $x_{0}$ such that $f'(x_{0}) \neq 0$ (B) $f$ has exactly one real root $x_{0}$ such that $f'(x_{0}) = 0$ (C) $f$ has $m$ distinct real roots (D) $f$ has no real root.
asked
Feb 20
in
Calculus
by
ankitgupta.1729
Boss
(
11.3k
points)

122
views
engineeringmathematics
calculus
userisi2015
usermod
+1
vote
6
answers
16
GATE201913
Compute $\lim_{x \rightarrow 3} \frac{x^481}{2x^25x3}$ $1$ $53/12$ $108/7$ Limit does not exist
asked
Feb 7
in
Calculus
by
Arjun
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400k
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1.6k
views
gate2019
engineeringmathematics
calculus
limits
0
votes
0
answers
17
How to solve such question.
$\frac{d}{dx}\int_{1}^{x^4} sect\space dt$
asked
Jan 20
in
Calculus
by
`JEET
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3.4k
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86
views
calculus
integration
0
votes
0
answers
18
MadeEasy Workbook: Calculus  Maxima Minima
asked
Jan 19
in
Calculus
by
chanchala3993
(
7
points)

45
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engineeringmathematics
calculus
maximaminima
madeeasybooklet
0
votes
0
answers
19
Calculating average mean
The aggregate monthly expenditure of a family was $ 6240 during first 3 months, $ 6780 during next 4 months, and $7236 during last 5 months of a year. If total saving during the year is $ 7080. Find average monthly income of family?
asked
Jan 13
in
Calculus
by
Alina
(
27
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33
views
0
votes
0
answers
20
Ace Test Series: Calculus  Integration
Can anyone help me with solving this type of problem? I want some resource from where I can learn to solve this type on integration, as according to solution it is a function of α, so I did not understand the solution.
asked
Jan 12
in
Calculus
by
jhaanuj2108
(
227
points)

67
views
acetestseries
calculus
integration
0
votes
1
answer
21
How to solve such question with different variable in the limit.
$\int_{a}^{x} \frac{sint}{t} dt$ (x > 0), then f(x) has _________________. (A) a maximum at x = $n\pi$ where n is even (B) a minimum at x = $n\pi$ where n is odd (C) a maximum at x = $n\pi$ where n is odd (D) a minimum at x = $\frac{n\pi}{2}$ where n is odd.
asked
Jan 11
in
Calculus
by
`JEET
Active
(
3.4k
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63
views
0
votes
1
answer
22
ME TEST SERIES
asked
Jan 10
in
Calculus
by
Shankar Kakde
(
373
points)

53
views
0
votes
1
answer
23
Integration
How to solve it?
asked
Jan 8
in
Calculus
by
ghostman23111
(
135
points)

58
views
+1
vote
1
answer
24
UPPCL AE 2018:85
asked
Jan 5
in
Calculus
by
Lakshman Patel RJIT
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36.3k
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93
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uppcl2018
0
votes
1
answer
25
UPPCL AE 2018:81
asked
Jan 5
in
Calculus
by
Lakshman Patel RJIT
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36.3k
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49
views
uppcl2018
0
votes
1
answer
26
self doubt
$\lim_{x\rightarrow \frac{\pi }{2}}cosx^{cosx}$ can we straight away say $0^{0}=0$ ?
asked
Jan 5
in
Calculus
by
manisha11
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2.1k
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48
views
calculus
0
votes
1
answer
27
calculus question
Question Number 4?
asked
Jan 4
in
Calculus
by
pradeepchaudhary
Active
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1.2k
points)

45
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calculus
0
votes
0
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28
#integration
I=$\int_{1}^{\infty }a^{ceil (log _{b} x ) } dx$
asked
Jan 3
in
Calculus
by
amit166
Junior
(
761
points)

47
views
integration
0
votes
0
answers
29
#integration
$I=\int sin(2x) cos(3x) dx$ 1.(5cosxcos5x)/10 2.(5sinxsin5x)/10 3.both 4.none
asked
Jan 3
in
Calculus
by
amit166
Junior
(
761
points)

66
views
integration
0
votes
0
answers
30
Math doubt
Is it true $\frac{1}{1+x^{2}}=1x^{2}$ Is it applied every function? (like limit func, generating func)?
asked
Jan 3
in
Calculus
by
srestha
Veteran
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114k
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54
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discretemathematics
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