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Recent questions and answers in Calculus
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TIFR2014A18
We are given a collection of real numbers where a real number $a_{i}\neq 0$ occurs $n_{i}$ times. Let the collection be enumerated as $\left\{x_{1}, x_{2},...x_{n}\right\}$ so that $x_{1}=x_{2}=...=x_{n_{1}}=a_{1}$ and so on, and $n=\sum _{i}n_{i}$ is finite. What is ... $\min_{i} a_{i}$ $\min_{i} \left(n_{i}a_{i}\right)$ $\max_{i} a_{i}$ None of the above.
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ago
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Calculus
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Arjun
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tifr2014
limits
+2
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2
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2
TIFR2019A13
Consider the integral $\int^{1}_{0} \frac{x^{300}}{1+x^2+x^3} dx$ What is the value of this integral correct up to two decimal places? $0.00$ $0.02$ $0.10$ $0.33$ $1.00$
answered
Jun 9
in
Calculus
by
Arjun
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209
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tifr2019
engineeringmathematics
calculus
integration
+19
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3
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3
GATE201416
Let the function ... There exists $\theta \in (\frac{\pi}{6},\frac{\pi}{3})$ such that $f'(\theta)\neq 0$ I only II only Both I and II Neither I Nor II
answered
Jun 8
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Calculus
by
97apoorva singh
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77
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3.5k
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gate20141
calculus
differentiability
normal
0
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1
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4
Differentiability
$\varphi \left ( x \right )=x^{2}\cos \frac{1}{x}$ when $x\neq 0$ $=0$ when $x=0$ Is it differentiable at $x=0$? Is it continuous ?
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Jun 7
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Calculus
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ankitgupta.1729
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51
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calculus
discretemathematics
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5
Maths: Limits
$\LARGE \lim_{n \rightarrow \infty} \frac{n^{\frac{3}{4}}}{log^9 n}$
answered
May 27
in
Calculus
by
Mk Utkarsh
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34.5k
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96
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engineeringmathematics
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+12
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5
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6
GATE201514
$\lim_{x\rightarrow \infty } x^{ \tfrac{1}{x}}$ is $\infty $ 0 1 Not defined
answered
May 26
in
Calculus
by
SALIL KUMAR
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11
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2k
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gate20151
calculus
limits
normal
+3
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1
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7
Limits
answered
May 16
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Calculus
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Satbir
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93
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limits
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+3
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1
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8
MadeEasy Test Series 2018: Calculus  Limits
The value of $\lim_{x\rightarrow \infty }\left ( \frac{4^{x+2} + 3^{x}}{4^{x2}} \right )$ is ____________
answered
May 16
in
Calculus
by
Satbir
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13.2k
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139
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engineeringmathematics
calculus
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madeeasytestseries
+2
votes
6
answers
9
GATE201913
Compute $\lim_{x \rightarrow 3} \frac{x^481}{2x^25x3}$ $1$ $53/12$ $108/7$ Limit does not exist
answered
May 13
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Calculus
by
Bikki_gupta
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77
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1.6k
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gate2019
engineeringmathematics
calculus
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0
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1
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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 $x_2$
answered
May 13
in
Calculus
by
pratekag
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387
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isi2019
engineeringmathematics
calculus
0
votes
0
answers
11
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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40.5k
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28
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isi2018
engineeringmathematics
calculus
continuity
0
votes
0
answers
12
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.
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May 11
in
Calculus
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akash.dinkar12
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40.5k
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17
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isi2018
engineeringmathematics
calculus
maximaminima
0
votes
0
answers
13
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
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41
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isi2018
engineeringmathematics
calculus
integration
0
votes
1
answer
14
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 $i = 1, 2, . . . , n.$ ... $a_n \rightarrow p, b_n \rightarrow p,c_n \rightarrow 12p$ $a_n \rightarrow1/2, b_n \rightarrow1/2,c_n \rightarrow0$ $a_n \rightarrow0, b_n \rightarrow0,c_n \rightarrow1$
answered
May 11
in
Calculus
by
srestha
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(
111k
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25
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isi2018
engineeringmathematics
calculus
limits
+1
vote
1
answer
15
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
May 7
in
Calculus
by
pratekag
Active
(
2k
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227
views
isi2019
engineeringmathematics
calculus
limits
+1
vote
1
answer
16
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 $\frac{1}{2^91}\\$ $\frac{10}{2^9+1}\\$ $\frac{10}{2^{10}1}\\$ $\frac{1}{2^{10}+1}$
answered
May 7
in
Calculus
by
pratekag
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(
2k
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338
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isi2019
engineeringmathematics
discretemathematics
settheory&algebra
functions
0
votes
1
answer
17
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 $1/4$ $1/6$ $1/8$ $1/24$
answered
May 7
in
Calculus
by
pratekag
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637
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isi2019
calculus
engineeringmathematics
0
votes
1
answer
18
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 $f(0)$ $f’(0)$ $f’’(0)$ $f(100)$
answered
May 7
in
Calculus
by
pratekag
Active
(
2k
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374
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isi2019
engineeringmathematics
calculus
integration
0
votes
1
answer
19
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 $(0,2)$
answered
May 7
in
Calculus
by
pratekag
Active
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2k
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216
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isi2019
engineeringmathematics
calculus
integration
0
votes
1
answer
20
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 $5$ $3$ $3$ $5$
answered
May 6
in
Calculus
by
pratekag
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2k
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151
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isi2019
calculus
limits
0
votes
0
answers
21
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
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Calculus
by
balchandar reddy san
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52
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engineeringmathematics
usergate2002
usermod
calculus
differentiability
+1
vote
1
answer
22
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.
answered
Mar 18
in
Calculus
by
Kushagra Chatterjee
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9.5k
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109
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sequenceseries
calculus
0
votes
1
answer
23
UPPCL AE 2018:81
answered
Mar 11
in
Calculus
by
Ram Swaroop
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3k
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52
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uppcl2018
+1
vote
1
answer
24
Continuity and Differentiability
If the function f(x) =[(x2)3 /a] sin(x2) + acos(x2), [.] denotes greatest integer function, is continuous & differentiable in (4,6) then find ‘a’ range: (A) a ϵ (∞,∞) (B) a ϵ [64, ∞) (C) a ϵ [128, ∞) (D) Not defined
answered
Mar 10
in
Calculus
by
jinal99
(
37
points)

310
views
0
votes
2
answers
25
ISRO2012ECE Engineering Mathematics
a) 1x b) (1x)/x c)1/x d)x/(1x)
answered
Mar 10
in
Calculus
by
abhishekmehta4u
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33.9k
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71
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engineeringmathematics
isro2012ece
isroece
calculus
0
votes
1
answer
26
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 $0$
answered
Feb 21
in
Calculus
by
venkatesh pagadala
(
495
points)

133
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engineeringmathematics
calculus
userisi2015
usermod
sequenceseries
limits
+1
vote
1
answer
27
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.
answered
Feb 21
in
Calculus
by
Kushagra Chatterjee
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9.5k
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125
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engineeringmathematics
calculus
userisi2015
usermod
+2
votes
3
answers
28
VALUE OF LIMIT
What is value of $\lim_{x\rightarrow 0, Y\rightarrow 0}\frac{xY}{x^2+Y^2}$ 1 1 0 Does not exist
answered
Jan 28
in
Calculus
by
Sai Shravan
(
169
points)

291
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limits
+5
votes
3
answers
29
TIFR2011A11
$\int_{0}^{1} \ln x\, \mathrm{d}x=$ $1$ $1$ $\infty $ $\infty $ None of the above.
answered
Jan 26
in
Calculus
by
Lakshman Patel RJIT
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(
40k
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469
views
tifr2011
calculus
integration
0
votes
0
answers
30
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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3.3k
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88
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calculus
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0
votes
0
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31
MadeEasy Workbook: Calculus  Maxima Minima
asked
Jan 19
in
Calculus
by
chanchala3993
(
5
points)

52
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engineeringmathematics
calculus
maximaminima
madeeasybooklet
0
votes
0
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32
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
(
9
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35
views
0
votes
0
answers
33
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
(
185
points)

73
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acetestseries
calculus
integration
0
votes
1
answer
34
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.
answered
Jan 12
in
Calculus
by
Pranavapp
(
21
points)

65
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0
votes
1
answer
35
Integration
How to solve it?
answered
Jan 11
in
Calculus
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adeemajain
(
193
points)

61
views
0
votes
1
answer
36
ME TEST SERIES
answered
Jan 10
in
Calculus
by
Kunal Kadian
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2.7k
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52
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+1
vote
1
answer
37
UPPCL AE 2018:85
answered
Jan 5
in
Calculus
by
Lakshman Patel RJIT
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40k
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94
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uppcl2018
0
votes
1
answer
38
self doubt
$\lim_{x\rightarrow \frac{\pi }{2}}cosx^{cosx}$ can we straight away say $0^{0}=0$ ?
answered
Jan 5
in
Calculus
by
Nandkishor3939
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50
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calculus
0
votes
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39
calculus question
Question Number 4?
answered
Jan 5
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Calculus
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GATE2021
(
11
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46
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calculus
0
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1
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40
GATE 2013 MA Calculus
answered
Jan 3
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Calculus
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