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Recent questions and answers in Calculus
0
votes
0
answers
1
Maths for natural science
Determine the domain of the function $f(x)=\left | x \right |+1$
Hailemariam
asked
in
Calculus
Aug 5
by
Hailemariam
46
views
calculus
functions
0
votes
0
answers
2
Mathematics for Natural Science
Determine the domain of the function $f(x) = |x – 2|$
Hailemariam
asked
in
Calculus
Aug 3
by
Hailemariam
41
views
calculus
0
votes
0
answers
3
Mathematics for Natural Science
Sketch the graph of $f(x) = \frac{x^{3}-1}{x^{2}-1}$
kidussss
asked
in
Calculus
Jul 29
by
kidussss
72
views
calculus
0
votes
2
answers
4
Applied Mathematics Calculus and Limit Question
Evaluate the question of the following limits. $\lim_{x\rightarrow 1} \frac{x}{(x-1)^{2}}$
ASNR1010
answered
in
Calculus
Jul 9
by
ASNR1010
251
views
limits
calculus
0
votes
2
answers
5
Applied Mathematics Calculus and Limit Question
Evaluate the question of the following limits. $\lim_{x\rightarrow \infty} \frac{2x^{3}+3x-5}{5x^{3}+1}$
Kabir5454
answered
in
Calculus
Jul 9
by
Kabir5454
74
views
calculus
limits
0
votes
1
answer
6
Applied Mathematics Derivative
Please find derivation of the following equation. Let $f(x)=e^{x^{2}}\ln x,$ then find, ${f}'(x)$.
Kabir5454
answered
in
Calculus
Jul 9
by
Kabir5454
48
views
calculus
differentiation
0
votes
2
answers
7
Applied Mathematics Question
Let $f(x) = e^{x^2},$ then find $f''(x).$
ASNR1010
answered
in
Calculus
Jul 8
by
ASNR1010
69
views
calculus
differentiation
2
votes
3
answers
8
Integration
Solve the following $\int_{0}^{\infty}e^{-x^2}x^4dx$
Kabir5454
answered
in
Calculus
May 18
by
Kabir5454
452
views
engineering-mathematics
integration
calculus
2
votes
2
answers
9
Gate 2014 CE Set 2
The expression $\lim_{a \to 0}\frac{x^{a}-1}{a}$ is equal to (A)$\log x$ (B)0 (c)$x\log x$ (D)$\infty$
Kabir5454
answered
in
Calculus
May 18
by
Kabir5454
1.6k
views
calculus
limits
gate-mathematics
23
votes
6
answers
10
GATE CSE 2010 | Question: 5
What is the value of $ \displaystyle\lim_{n \to \infty}\left(1 - \frac{1}{n}\right)^{2n}$ ? $0$ $e^{-2}$ $e^{-1/2}$ $1$
Kabir5454
answered
in
Calculus
May 17
by
Kabir5454
5.9k
views
gatecse-2010
calculus
limits
normal
19
votes
5
answers
11
GATE IT 2008 | Question: 31
If $f(x)$ is defined as follows, what is the minimum value of $f(x)$ for $x \in (0, 2]$ ? $f(x) = \begin{cases} \frac{25}{8x} &\text{ when } x \leq \frac{3}{2} \\ x+ \frac{1}{x} &\text { otherwise}\end{cases}$ $2$ $2 \frac{1}{12}$ $2\frac{1}{6}$ $2\frac{1}{2}$
Kabir5454
answered
in
Calculus
May 17
by
Kabir5454
5.2k
views
gateit-2008
calculus
maxima-minima
normal
0
votes
0
answers
12
iit kanpur Calculas practice question
Does there exist a differentiable function f : [0, 2] → R satisfying f(0) = −1, f(2) = 4 and f’(x) ≤ 2 for all x ∈ [0, 2]?
Kabir5454
asked
in
Calculus
May 16
by
Kabir5454
77
views
calculus
1
vote
2
answers
13
ISI2015-DCG-45
The value of $\underset{x \to 0}{\lim} \dfrac{\tan ^2 x – x \tan x }{\sin x}$ is $\frac{\sqrt{3}}{2}$ $\frac{1}{2}$ $0$ None of these
Kabir5454
answered
in
Calculus
May 12
by
Kabir5454
175
views
isi2015-dcg
calculus
limits
0
votes
2
answers
14
NIELIT 2016 MAR Scientist B - Section B: 13
$\underset{x\to 0}{\lim} \dfrac{(1-\cos x)}{2}$ is equal to $0$ $1$ $1/3$ $1/2$
Kabir5454
answered
in
Calculus
May 11
by
Kabir5454
369
views
nielit2016mar-scientistb
engineering-mathematics
calculus
limits
0
votes
1
answer
15
Gilbert Strang
$\int_{}^{}\frac{x dx}{\sqrt{x^4-1}}$
Kabir5454
answered
in
Calculus
May 11
by
Kabir5454
209
views
gilbert-strang
calculus
engineering-mathematics
integration
2
votes
1
answer
16
ISI2016-MMA-20
Let $f : (0, \infty) \rightarrow (0, \infty)$ be a strictly decreasing function. Consider $h(x) = \dfrac{f(\frac{x}{1+x})}{1+f(\frac{x}{1+x})}$. Which one of the following is always true? $h$ is strictly decreasing $h$ is strictly increasing $h$ is strictly decreasing at first and then strictly increasing $h$ is strictly increasing at first and then strictly decreasing
Kabir5454
answered
in
Calculus
May 11
by
Kabir5454
179
views
isi2016-mmamma
calculus
functions
non-gate
0
votes
1
answer
17
Virtual Gate Test Series: Calculus
i have solved it by putting the values
Kabir5454
answered
in
Calculus
May 11
by
Kabir5454
208
views
engineering-mathematics
calculus
virtual-gate-test-series
0
votes
1
answer
18
ISI2018-DCG-28
Let $f(x)=e^{-\big( \frac{1}{x^2-3x+2} \big) };x\in \mathbb{R} \: \: \& x \notin \{1,2\}$. Let $a=\underset{n \to 1^+}{\lim}f(x)$ and $b=\underset{x \to 1^-}{\lim} f(x)$. Then $a=\infty, \: b=0$ $a=0, \: b=\infty$ $a=0, \: b=0$ $a=\infty, \: b=\infty$
Kabir5454
answered
in
Calculus
May 11
by
Kabir5454
160
views
isi2018-dcg
calculus
limits
functions
0
votes
1
answer
19
ISI2016-DCG-56
$\underset{x\rightarrow \infty}{\lim} \left(1+\dfrac{1}{x^{2}}\right)^{x}$ equals $-1$ $0$ $1$ Does not exist
Kabir5454
answered
in
Calculus
May 11
by
Kabir5454
128
views
isi2016-dcg
calculus
limits
1
vote
3
answers
20
ISI2015-MMA-20
The limit $\underset{n \to \infty}{\lim} \left( 1- \frac{1}{n^2} \right) ^n$ equals $e^{-1}$ $e^{-1/2}$ $e^{-2}$ $1$
Kabir5454
answered
in
Calculus
May 11
by
Kabir5454
385
views
isi2015-mma
calculus
limits
non-gate
1
vote
1
answer
21
ISI2014-DCG-21
Suppose that the function $h(x)$ is defined as $h(x)=g(f(x))$ where $g(x)$ is monotone increasing, $f(x)$ is concave, and $g’’(x)$ and $f’’(x)$ exist for all $x$. Then $h(x)$ is always concave always convex not necessarily concave None of these
Kabir5454
answered
in
Calculus
May 10
by
Kabir5454
275
views
isi2014-dcg
calculus
functions
maxima-minima
convex-concave
0
votes
1
answer
22
Calculus by Spivak 4th edition Chapter 10 problem 9
ankitgupta.1729
answered
in
Calculus
May 3
by
ankitgupta.1729
77
views
5
votes
3
answers
23
ISI2004-MIII: 13
Let $X =\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+\ldots+\frac{1}{3001}$. Then $X< 1$ $X>\frac{3}{2}$ $1< X< \frac{3}{2}$ none of the above
ankitgupta.1729
answered
in
Calculus
May 3
by
ankitgupta.1729
1.8k
views
isi2004
engineering-mathematics
integration
9
votes
2
answers
24
ISI2004-MIII: 12
The maximum possible value of $xy^2z^3$ subjected to condition $x,y,z \geq 0$ and $x+y+z=3$ is $1$ $\frac{9}{8}$ $\frac{9}{4}$ $\frac{27}{16}$
niks77
answered
in
Calculus
Apr 30
by
niks77
827
views
isi2004
engineering-mathematics
maxima-minima
1
vote
1
answer
25
ISI2015-MMA-77
Let $R$ be the triangle in the $xy$ – plane bounded by the $x$-axis, the line $y=x$, and the line $x=1$. The value of the double integral $ \int \int_R \frac{\sin x}{x}\: dxdy$ is $1-\cos 1$ $\cos 1$ $\frac{\pi}{2}$ $\pi$
niks77
answered
in
Calculus
Apr 29
by
niks77
277
views
isi2015-mma
integration
non-gate
0
votes
2
answers
26
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
s_dr_13
answered
in
Calculus
Mar 22
by
s_dr_13
565
views
nielit2017dec-assistanta
engineering-mathematics
calculus
continuity
0
votes
2
answers
27
NIELIT 2016 MAR Scientist B - Section B: 11
What is the derivative w.r.t $x$ of the function given by $\large \Phi(x)= \displaystyle \int_{0}^{x^2}\sqrt t\:dt$, $2x^2$ $\sqrt x$ $0$ $1$
s_dr_13
answered
in
Calculus
Mar 22
by
s_dr_13
323
views
nielit2016mar-scientistb
engineering-mathematics
calculus
integration
definite-integral
0
votes
2
answers
28
NIELIT 2016 MAR Scientist C - Section B: 13
$\displaystyle \lim_{x \rightarrow 0}\frac{1}{x^{6}} \displaystyle \int_{0}^{x^{2}}\frac{t^{2}dt}{t^{6}+1}=$? $1/4$ $1/3$ $1/2$ $1$
Anuj2000
answered
in
Calculus
Mar 16
by
Anuj2000
240
views
nielit2016mar-scientistc
calculus
1
vote
1
answer
29
ISI2015-DCG-56
$\underset{x \to \infty}{\lim} \left( 1 + \dfrac{1}{x^2} \right) ^x$ equals $-1$ $0$ $1$ Does not exist
preeti0448
answered
in
Calculus
Feb 27
by
preeti0448
203
views
isi2015-dcg
calculus
limits
1
vote
0
answers
30
#ISI2021
Let f(x-y) = $\frac{f(x)}{f(y)}$ for all x,y $\epsilon$ R and f’(0) = p, f’(5) = q. Then the value of f’(-5) is q -q $\frac{p}{q}$ $\frac{p^2}{q}$
Jeetu Bhaiya
asked
in
Calculus
Feb 24
by
Jeetu Bhaiya
91
views
3
votes
4
answers
31
GATE CSE 2022 | Question: 24
The value of the following limit is ________________. $\lim_{x \rightarrow 0^{+}} \frac{\sqrt{x}}{1-e^{2\sqrt{x}}}$
ankitgupta.1729
answered
in
Calculus
Feb 23
by
ankitgupta.1729
906
views
gatecse-2022
numerical-answers
calculus
limits
0
votes
0
answers
32
Global and Local Minimum
Suppose that we have an objective function X ⊆ R^n → R and Y ⊂ X. Which of the following are correct: Every global minimizer of f in X is global minimizer in Y Every local minimizer of f in Y is local minimizer in X My answer is that 1) and 2) are correct. I want to check if my answers are correct or we can prove something other with some example.
AlgoHuman
asked
in
Calculus
Feb 14
by
AlgoHuman
97
views
calculus
engineering-mathematics
maxima-minima
0
votes
1
answer
33
Made Easy Full length Test
Options Given were: (pi)/2 pi -(pi) none
Kabir5454
answered
in
Calculus
Jan 24
by
Kabir5454
149
views
1
vote
1
answer
34
Made Easy Test Series Engineering Maths
Dear Friends can any body tell me limit exists at 1 or not? as According to me the limit exists at 1 as both gives -1 at 1 but in madeeasy it’s given that the limit doesn’t exists...
LRU
answered
in
Calculus
Jan 18
by
LRU
153
views
1
vote
1
answer
35
me book mathematics
Which of following function is strictly bounded?
zeikion
answered
in
Calculus
Dec 1, 2021
by
zeikion
1.7k
views
0
votes
2
answers
36
Calculus self doubt
Calculus looks difficult for me. Any resources to learn calculus for GATE
wer 123
answered
in
Calculus
Nov 25, 2021
by
wer 123
181
views
engineering-mathematics
calculus
self-doubt
0
votes
0
answers
37
Applied Test Series
What is the correct procedure to solve this limit ?
LRU
asked
in
Calculus
Nov 5, 2021
by
LRU
161
views
test-series
engineering-mathematics
calculus
limits
4
votes
4
answers
38
TIFR2010-Maths-A-8
Let $f(x)= |x|^{3/2}, x \in \mathbb{R}$. Then $f$ is uniformly continuous. $f$ is continuous, but not differentiable at $x=0$. $f$ is differentiable and $f ' $ is continuous. $f$ is differentiable, but $f ' $ is discontinuous at $x=0$.
huny
answered
in
Calculus
Oct 9, 2021
by
huny
805
views
tifrmaths2010
calculus
differentiation
continuity
0
votes
0
answers
39
math book
$\int_{0}^{1}\tan^{-1} (1-\frac{1}{x})$ d(x) find
amit166
asked
in
Calculus
Sep 25, 2021
by
amit166
160
views
integration
0
votes
1
answer
40
#mathematics
What is the difference between Integration and Summation? Which one produces a greater value in the same range?
Nibchee
answered
in
Calculus
Sep 15, 2021
by
Nibchee
110
views
integration
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Recent questions and answers in Calculus
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