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Webpage for Calculus:
Recent questions tagged calculus
1
votes
3
answers
151
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 differentiableContinuous but not differentiableDifferentiable but not continuousNeith...
admin
1.1k
views
admin
asked
Mar 31, 2020
Calculus
nielit2017dec-assistanta
engineering-mathematics
calculus
continuity
+
–
3
votes
2
answers
152
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$$1,-8$
admin
664
views
admin
asked
Mar 31, 2020
Calculus
nielit2016mar-scientistb
engineering-mathematics
calculus
maxima-minima
+
–
1
votes
1
answer
153
NIELIT 2016 MAR Scientist B - Section B: 9
The value of improper integral $\displaystyle\int_{0}^{1} x\ln x =?$ $1/4$ $0$ $-1/4$ $1$
The value of improper integral $\displaystyle\int_{0}^{1} x\ln x =?$$1/4$$0$$-1/4$$1$
admin
735
views
admin
asked
Mar 31, 2020
Calculus
nielit2016mar-scientistb
engineering-mathematics
calculus
integration
definite-integral
+
–
1
votes
1
answer
154
NIELIT 2016 MAR Scientist B - Section B: 10
Maxima and minimum of the function $f(x)=2x^3-15x^2+36x+10$ occur; respectively at $x=3$ and $x=2$ $x=1$ and $x=3$ $x=2$ and $x=3$ $x=3$ and $x=4$
Maxima and minimum of the function $f(x)=2x^3-15x^2+36x+10$ occur; respectively at $x=3$ and $x=2$$x=1$ and $x=3$$x=2$ and $x=3$$x=3$ and $x=4$
admin
563
views
admin
asked
Mar 31, 2020
Calculus
nielit2016mar-scientistb
engineering-mathematics
calculus
maxima-minima
+
–
1
votes
2
answers
155
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$$1$
admin
542
views
admin
asked
Mar 31, 2020
Calculus
nielit2016mar-scientistb
engineering-mathematics
calculus
integration
definite-integral
+
–
1
votes
2
answers
156
NIELIT 2016 MAR Scientist B - Section B: 13
$\underset{x\to 0}{\lim} \dfrac{(1-\cos x)}{2}$ is equal to $0$ $1$ $1/3$ $1/2$
$\underset{x\to 0}{\lim} \dfrac{(1-\cos x)}{2}$ is equal to$0$$1$$1/3$$1/2$
admin
610
views
admin
asked
Mar 31, 2020
Calculus
nielit2016mar-scientistb
engineering-mathematics
calculus
limits
+
–
0
votes
1
answer
157
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$$-2$
admin
566
views
admin
asked
Mar 31, 2020
Calculus
nielit2016mar-scientistb
engineering-mathematics
calculus
maxima-minima
+
–
1
votes
1
answer
158
NIELIT 2016 DEC Scientist B (CS) - Section B: 26
Consider the function $f(x)=\sin(x)$ in the interval $\bigg [\dfrac{ \pi}{4},\dfrac{7\pi}{4}\bigg ]$. The number and location(s) of the minima of this function are: One, at $\dfrac{\pi}{2} \\$ One, at $\dfrac{3\pi}{2} \\$ Two, at $\dfrac{\pi}{2}$ and $\dfrac{3\pi}{2} \\$ Two, at $\dfrac{\pi}{4}$ and $\dfrac{3\pi}{2}$
Consider the function $f(x)=\sin(x)$ in the interval $\bigg [\dfrac{ \pi}{4},\dfrac{7\pi}{4}\bigg ]$. The number and location(s) of the minima of this function are:One...
admin
601
views
admin
asked
Mar 31, 2020
Calculus
nielit2016dec-scientistb-cs
engineering-mathematics
calculus
maxima-minima
+
–
23
votes
3
answers
159
GATE CSE 2020 | Question: 1
Consider the functions $e^{-x}$ $x^{2}-\sin x$ $\sqrt{x^{3}+1}$ Which of the above functions is/are increasing everywhere in $[ 0,1]$? Ⅲ only Ⅱ only Ⅱ and Ⅲ only Ⅰ and Ⅲ only
Consider the functions $e^{-x}$$x^{2}-\sin x$$\sqrt{x^{3}+1}$Which of the above functions is/are increasing everywhere in $[ 0,1]$?Ⅲ onlyⅡ onlyⅡ and Ⅲ onlyⅠ a...
Arjun
12.3k
views
Arjun
asked
Feb 12, 2020
Calculus
gatecse-2020
engineering-mathematics
calculus
maxima-minima
1-mark
+
–
0
votes
2
answers
160
TIFR CSE 2020 | Part B | Question: 4
A $\textit{clamp}$ gate is an analog gate parametrized by two real numbers $a$ and $b$, and denoted as $\text{clamp}_{a,b}$. It takes as input two non-negative real numbers $x$ and $y$ ... outputs the maximum of $x$ and $y?$ $1$ $2$ $3$ $4$ No circuit composed only of clamp gates can compute the max function
A $\textit{clamp}$ gate is an analog gate parametrized by two real numbers $a$ and $b$, and denoted as $\text{clamp}_{a,b}$. It takes as input two non-negative real numbe...
admin
799
views
admin
asked
Feb 10, 2020
Calculus
tifr2020
calculus
maxima-minima
+
–
0
votes
2
answers
161
TIFR CSE 2020 | Part A | Question: 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'$ and and second ... 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 $...
admin
1.3k
views
admin
asked
Feb 10, 2020
Calculus
tifr2020
engineering-mathematics
calculus
maxima-minima
+
–
3
votes
1
answer
162
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...
Arjun
828
views
Arjun
asked
Sep 23, 2019
Calculus
isi2014-dcg
calculus
limits
+
–
4
votes
4
answers
163
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}$
Arjun
1.5k
views
Arjun
asked
Sep 23, 2019
Calculus
isi2014-dcg
calculus
limits
+
–
3
votes
4
answers
164
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$$1$
Arjun
1.2k
views
Arjun
asked
Sep 23, 2019
Calculus
isi2014-dcg
calculus
limits
+
–
2
votes
2
answers
165
ISI2014-DCG-6
If $f(x)$ is a real valued function such that $2f(x)+3f(-x)=15-4x$, for every $x \in \mathbb{R}$, then $f(2)$ is $-15$ $22$ $11$ $0$
If $f(x)$ is a real valued function such that $2f(x)+3f(-x)=15-4x$, for every $x \in \mathbb{R}$, then $f(2)$ is$-15$$22$$11$$0$
Arjun
515
views
Arjun
asked
Sep 23, 2019
Calculus
isi2014-dcg
calculus
functions
+
–
2
votes
3
answers
166
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 $f(x)$ isthe interval $[-1 , \sqrt{3}{/2}]$the interval $[-\sqrt{3}{/2}, 1]$the interval $[-1, 1]$none of...
Arjun
584
views
Arjun
asked
Sep 23, 2019
Calculus
isi2014-dcg
calculus
functions
range
+
–
2
votes
1
answer
167
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
Arjun
724
views
Arjun
asked
Sep 23, 2019
Calculus
isi2014-dcg
calculus
definite-integral
integration
+
–
2
votes
1
answer
168
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$$f(x)$ is di...
Arjun
563
views
Arjun
asked
Sep 23, 2019
Calculus
isi2014-dcg
calculus
differentiation
+
–
2
votes
3
answers
169
ISI2014-DCG-17
$\underset{x \to 2}{\lim} \dfrac{1}{1+e^{\frac{1}{x-2}}}$ is $0$ $1/2$ $1$ non-existent
$\underset{x \to 2}{\lim} \dfrac{1}{1+e^{\frac{1}{x-2}}}$ is$0$$1/2$$1$non-existent
Arjun
628
views
Arjun
asked
Sep 23, 2019
Calculus
isi2014-dcg
calculus
limits
+
–
3
votes
1
answer
170
ISI2014-DCG-19
It is given that $e^a+e^b=10$ where $a$ and $b$ are real. Then the maximum value of $(e^a+e^b+e^{a+b}+1)$ is $36$ $\infty$ $25$ $21$
It is given that $e^a+e^b=10$ where $a$ and $b$ are real. Then the maximum value of $(e^a+e^b+e^{a+b}+1)$ is$36$$\infty$$25$$21$
Arjun
513
views
Arjun
asked
Sep 23, 2019
Calculus
isi2014-dcg
calculus
maxima-minima
+
–
0
votes
1
answer
171
ISI2014-DCG-20
If $A(t)$ is the area of the region bounded by the curve $y=e^{-\mid x \mid}$ and the portion of the $x$-axis between $-t$ and $t$, then $\underset{t \to \infty}{\lim} A(t)$ equals $0$ $1$ $2$ $4$
If $A(t)$ is the area of the region bounded by the curve $y=e^{-\mid x \mid}$ and the portion of the $x$-axis between $-t$ and $t$, then $\underset{t \to \infty}{\lim} A(...
Arjun
343
views
Arjun
asked
Sep 23, 2019
Geometry
isi2014-dcg
calculus
definite-integral
area
+
–
1
votes
1
answer
172
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
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 $x$....
Arjun
476
views
Arjun
asked
Sep 23, 2019
Calculus
isi2014-dcg
calculus
functions
maxima-minima
convex-concave
+
–
0
votes
1
answer
173
ISI2014-DCG-24
Let $f(x) = \dfrac{2x}{x-1}, \: x \neq 1$. State which of the following statements is true. For all real $y$, there exists $x$ such that $f(x)=y$ For all real $y \neq 1$, there exists $x$ such that $f(x)=y$ For all real $y \neq 2$, there exists $x$ such that $f(x)=y$ None of the above is true
Let $f(x) = \dfrac{2x}{x-1}, \: x \neq 1$. State which of the following statements is true.For all real $y$, there exists $x$ such that $f(x)=y$For all real $y \neq 1$, ...
Arjun
420
views
Arjun
asked
Sep 23, 2019
Calculus
isi2014-dcg
calculus
functions
+
–
2
votes
2
answers
174
ISI2014-DCG-28
The area enclosed by the curve $\mid\: x \mid + \mid y \mid =1$ is $1$ $2$ $\sqrt{2}$ $4$
The area enclosed by the curve $\mid\: x \mid + \mid y \mid =1$ is$1$$2$$\sqrt{2}$$4$
Arjun
511
views
Arjun
asked
Sep 23, 2019
Calculus
isi2014-dcg
calculus
area-under-the-curve
+
–
0
votes
2
answers
175
ISI2014-DCG-29
If $f(x) = \sin \bigg( \dfrac{1}{x^2+1} \bigg),$ then $f(x)$ is continuous at $x=0$, but not differentiable at $x=0$ $f(x)$ is differentiable at $x=0$, and $f’(0) \neq 0$ $f(x)$ is differentiable at $x=0$, and $f’(0) = 0$ None of the above
If $f(x) = \sin \bigg( \dfrac{1}{x^2+1} \bigg),$ then$f(x)$ is continuous at $x=0$, but not differentiable at $x=0$$f(x)$ is differentiable at $x=0$, and $f’(0) \neq 0$...
Arjun
721
views
Arjun
asked
Sep 23, 2019
Calculus
isi2014-dcg
calculus
continuity
differentiation
+
–
3
votes
1
answer
176
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{[\alph...
Arjun
583
views
Arjun
asked
Sep 23, 2019
Calculus
isi2014-dcg
calculus
integration
definite-integral
+
–
1
votes
0
answers
177
ISI2014-DCG-33
Let $f(x)$ be a continuous function from $[0,1]$ to $[0,1]$ satisfying the following properties. $f(0)=0$, $f(1)=1$, and $f(x_1)<f(x_2)$ for $x_1 < x_2$ with $0 < x_1, \: x_2<1$. Then the number of such functions is $0$ $1$ $2$ $\infty$
Let $f(x)$ be a continuous function from $[0,1]$ to $[0,1]$ satisfying the following properties.$f(0)=0$,$f(1)=1$, and$f(x_1)<f(x_2)$ for $x_1 < x_2$ with $0 < x_1, \: x_...
Arjun
478
views
Arjun
asked
Sep 23, 2019
Calculus
isi2014-dcg
calculus
functions
limits
+
–
2
votes
2
answers
178
ISI2014-DCG-37
Let $f: \bigg( – \dfrac{\pi}{2}, \dfrac{\pi}{2} \bigg) \to \mathbb{R}$ be a continuous function, $f(x) \to +\infty$ as $x \to \dfrac{\pi^-}{2}$ and $f(x) \to – \infty$ as $x \to -\dfrac{\pi^+}{2}$. Which one of the following functions satisfies the above properties of $f(x)$? $\cos x$ $\tan x$ $\tan^{-1} x$ $\sin x$
Let $f: \bigg( – \dfrac{\pi}{2}, \dfrac{\pi}{2} \bigg) \to \mathbb{R}$ be a continuous function, $f(x) \to +\infty$ as $x \to \dfrac{\pi^-}{2}$ and $f(x) \to – \infty...
Arjun
580
views
Arjun
asked
Sep 23, 2019
Calculus
isi2014-dcg
calculus
functions
limits
continuity
+
–
1
votes
1
answer
179
ISI2014-DCG-39
The function $f(x) = x^{1/x}, \: x \neq 0$ has a minimum at $x=e$; a maximum at $x=e$; neither a maximum nor a minimum at $x=e$; None of the above
The function $f(x) = x^{1/x}, \: x \neq 0$ hasa minimum at $x=e$;a maximum at $x=e$;neither a maximum nor a minimum at $x=e$;None of the above
Arjun
577
views
Arjun
asked
Sep 23, 2019
Calculus
isi2014-dcg
maxima-minima
calculus
+
–
0
votes
0
answers
180
ISI2014-DCG-42
Let $f(x)=\sin x^2, \: x \in \mathbb{R}$. Then $f$ has no local minima $f$ has no local maxima $f$ has local minima at $x=0$ and $x=\pm\sqrt{(k+\frac{1}{2} ) \pi}$ for odd integers $k$ and local maxima at $x=\pm\sqrt{(k+\frac{1}{2} ) \pi}$ for even integers $k$ None of the above
Let $f(x)=\sin x^2, \: x \in \mathbb{R}$. Then$f$ has no local minima$f$ has no local maxima$f$ has local minima at $x=0$ and $x=\pm\sqrt{(k+\frac{1}{2} ) \pi}$ for odd i...
Arjun
410
views
Arjun
asked
Sep 23, 2019
Calculus
isi2014-dcg
calculus
maxima-minima
+
–
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