Register

Recent questions tagged calculus

0 votes
0 answers
42
GATE ECE 2016 Set 3 | Question: 4
The integral $\int\limits_{0}^{1}\large\frac{dx}{\sqrt{(1-x)}}$ is equal to _______
The integral $\int\limits_{0}^{1}\large\frac{dx}{\sqrt{(1-x)}}$ is equal to _______
0 votes
0 answers
44
GATE ECE 2016 Set 2 | Question: 4
How many distinct value of $x$ satisfy the equation $\sin(x)=x/2$, where $x$ is in radians? $1$ $2$ $3$ $4$ or more
How many distinct value of $x$ satisfy the equation $\sin(x)=x/2$, where $x$ is in radians?$1$$2$$3$$4$ or more
0 votes
0 answers
46
GATE ECE 2016 Set 1 | Question: 26
The integral $\frac{1}{2\pi} \iint_D(x+y+10) \,dx\,dy$, where $D$ denotes the disc: $x^2+y^2\leq 4$,evaluates to _________
The integral $\frac{1}{2\pi} \iint_D(x+y+10) \,dx\,dy$, where $D$ denotes the disc: $x^2+y^2\leq 4$,evaluates to _________
0 votes
0 answers
47
GATE ECE 2015 Set 3 | Question: 2
The contour on the $x-y$ plane, where the partial derivative of $x^{2} + y^{2}$ with respect to $y$ is equal to the partial derivative of $6y+4x$ with respect to $x$, is $y=2$ $x=2$ $x+y=4$ $x-y=0$
The contour on the $x-y$ plane, where the partial derivative of $x^{2} + y^{2}$ with respect to $y$ is equal to the partial derivative of $6y+4x$ with respect to $x$, is$...
0 votes
0 answers
48
GATE ECE 2015 Set 3 | Question: 5
The value of $\displaystyle{}\sum_{n=0}^{\infty} n \left(\dfrac{1}{2}\right)^{n}$ is ________.
The value of $\displaystyle{}\sum_{n=0}^{\infty} n \left(\dfrac{1}{2}\right)^{n}$ is ________.
0 votes
0 answers
49
GATE ECE 2015 Set 2 | Question: 27
The value of the integral $\int_{-\infty}^{\infty} 12\cos(2\pi t) \dfrac{\sin(4\pi t)}{4 \pi t}dt$ is _________.
The value of the integral $\int_{-\infty}^{\infty} 12\cos(2\pi t) \dfrac{\sin(4\pi t)}{4 \pi t}dt$ is _________.
0 votes
0 answers
50
GATE ECE 2015 Set 1 | Question: 2
A function $f(x)=1-x^2+x^3$ is defined in the closed interval $[-1,1]$. The value of $x$, in the open interval $(-1,1)$ for which the mean value theorem is satisfied, is $-1/2$ $-1/3$ $1/3$ $1/2$
A function $f(x)=1-x^2+x^3$ is defined in the closed interval $[-1,1]$. The value of $x$, in the open interval $(-1,1)$ for which the mean value theorem is satisfied, is$...
0 votes
0 answers
51
GATE ECE 2015 Set 1 | Question: 28
Which one of the following graphs describes the function $f(x)=e^{-x}(x^2+x+1)$?
Which one of the following graphs describes the function $f(x)=e^{-x}(x^2+x+1)$?
0 votes
0 answers
52
GATE ECE 2015 Set 1 | Question: 29
The maximum area (in square units) of a rectangle whose vertices lie on the eclipse $x^2+4y^2=1$ is __________.
The maximum area (in square units) of a rectangle whose vertices lie on the eclipse $x^2+4y^2=1$ is __________.
0 votes
0 answers
53
GATE ECE 2014 Set 4 | Question: 1
The series $\Sigma_{n=0}^{\infty} \frac{1}{n!}$ converges to $2 \text{ ln } 2$ $\sqrt{2}$ $2$ $e$
The series $\Sigma_{n=0}^{\infty} \frac{1}{n!}$ converges to$2 \text{ ln } 2$$\sqrt{2}$$2$$e$
0 votes
0 answers
54
GATE ECE 2014 Set 4 | Question: 29
For a right angled triangle, if the sum of the lengths of the hypotenuse and a side is kept constant, in order to have maximum area of the triangle, the triangle, the angle between the hypotenuse and the side is $12^{\circ}$ $36^{\circ}$ $60^{\circ}$ $45^{\circ}$
For a right angled triangle, if the sum of the lengths of the hypotenuse and a side is kept constant, in order to have maximum area of the triangle, the triangle, the ang...
0 votes
0 answers
55
GATE ECE 2014 Set 3 | Question: 1
The maximum value of the function $f(x) = \text{ln } (1+x) – x $ (where $x >-1$) occurs at $x=$_______.
The maximum value of the function $f(x) = \text{ln } (1+x) – x $ (where $x >-1$) occurs at $x=$_______.
0 votes
0 answers
56
GATE ECE 2014 Set 3 | Question: 26
The maximum value of $f(x)$= $2x^{3}$ – $9x^{2}$ + $12x – 3$ in the interval $0\leq x\leq 3$ is _______.
The maximum value of $f(x)$= $2x^{3}$ – $9x^{2}$ + $12x – 3$ in the interval $0\leq x\leq 3$ is _______.
0 votes
0 answers
57
GATE ECE 2014 Set 2 | Question: 3
For $0 \leq t < \infty ,$ the maximum value of the function $f(t)= e^{-t}-2e^{-2t}$ occurs at $t= log_{e}4$ $t= log_{e}2$ $t= 0$ $t= log_{e}8$
For $0 \leq t < \infty ,$ the maximum value of the function $f(t)= e^{-t}-2e^{-2t}$ occurs at$t= log_{e}4$$t= log_{e}2$$t= 0$$t= log_{e}8$
0 votes
0 answers
58
GATE ECE 2014 Set 2 | Question: 4
The value of $\lim_{x\rightarrow \infty }(1 +\tfrac{1}{x})^{x}$ is $\text{ln }2$ $1.0$ $e$ $\infty$
The value of $$\lim_{x\rightarrow \infty }(1 +\tfrac{1}{x})^{x}$$ is$\text{ln }2$$1.0$$e$$\infty$
0 votes
0 answers
59
GATE ECE 2014 Set 2 | Question: 45
The value of the integral $\int_{-\infty }^{\infty } \text{sinc}^{2}(5t) \: dt$ is _______.
The value of the integral $\int_{-\infty }^{\infty } \text{sinc}^{2}(5t) \: dt$ is _______.
0 votes
0 answers
60
GATE ECE 2014 Set 1 | Question: 26
The Taylor series expansion of $3\sin x + 2 \cos x$ is $2 + 3x-x^{2} – \frac{x^{3}}{2} + \dots$ $2 – 3x + x^{2} – \frac{x^{3}}{2} + \dots$ $2 + 3x + x^{2} + \frac{x^{3}}{2} + \dots$ $2 – 3x – x^{2} + \frac{x^{3}}{2} + \dots$
The Taylor series expansion of $3\sin x + 2 \cos x$ is$2 + 3x-x^{2} – \frac{x^{3}}{2} + \dots$$2 – 3x + x^{2} – \frac{x^{3}}{2} + \dots$$2 + 3x + x^{2} + \frac...
0 votes
0 answers
61
GATE ECE 2013 | Question: 20
A polynomial $f(x) = a_{4}x^{4} + a_{3}x^{3} + a_{2}x^{2} + a_{1}x - a_{0}$ with all coefficients positive has no real roots no negative real root odd number of real roots at least one positive and one negative real root
A polynomial $f(x) = a_{4}x^{4} + a_{3}x^{3} + a_{2}x^{2} + a_{1}x - a_{0}$ with all coefficients positive hasno real rootsno negative real rootodd number of real roots a...
0 votes
0 answers
62
GATE ECE 2012 | Question: 46
The maximum value of $f(x)=x^3-9x^2+24x+5$ in the interval $[1,6]$ is $21$ $25$ $41$ $46$
The maximum value of $f(x)=x^3-9x^2+24x+5$ in the interval $[1,6]$ is$21$$25$$41$$46$
0 votes
0 answers
63
GATE ECE 2012 | Question: 25
If $x=\sqrt{-1}$, then the value of $x^x$ is $e^{\frac{-\pi}{2}}$ $e^{\frac{\pi}{2}}$ $x$ $1$
If $x=\sqrt{-1}$, then the value of $x^x$ is$e^{\frac{-\pi}{2}}$$e^{\frac{\pi}{2}}$$x$$1$
0 votes
0 answers
64
GATE ECE 2018 | Question: 55
Let $X\left[ k \right ] = k + 1,0\leq k\leq 7$ be $8$-point $\:\text{DFT}\:$ of a sequence $x[n]$. where $X\left [ k \right ]=\sum_{n=0}^{N-1}x \left [ n \right ]e^{-j2\pi nk/N}$. The value (correct to two decimal places) of $\sum_{n=0}^{3}x \left [ 2n \right ]$ is ________.
Let $X\left[ k \right ] = k + 1,0\leq k\leq 7$ be $8$-point $\:\text{DFT}\:$ of a sequence $x[n]$.where $X\left [ k \right ]=\sum_{n=0}^{N-1}x \left [ n \right ]e^{-j2\pi...
0 votes
0 answers
65
GATE ECE 2018 | Question: 52
Let $r=x^{2}+y-z$ and $z^{3}-xy+yz+y^{3}=1.$ Assume that $x$ and $y$ are independent variables. At $\left( x,y,z \right)=\left ( 2,-1,1 \right ),$ the value (correct to two decimal places) of $\dfrac{\partial r}{\partial x}$ is _________ .
Let $r=x^{2}+y-z$ and $z^{3}-xy+yz+y^{3}=1.$ Assume that $x$ and $y$ are independent variables. At $\left( x,y,z \right)=\left ( 2,-1,1 \right ),$ the value (correct to t...
0 votes
0 answers
66
GATE ECE 2018 | Question: 24
Taylor series expansion of $f\left ( x \right )=\int ^{x}_{0}e^{-\left ( \frac{t^{2}}{2} \right )}dt$ around $x=0$ has the form $f\left ( x \right )={a}_{0}+a_{1}x+a_{2}x^{2}+...$ The coefficient $a_{2}$ (correct to two decimal places) is equal to ________.
Taylor series expansion of $f\left ( x \right )=\int ^{x}_{0}e^{-\left ( \frac{t^{2}}{2} \right )}dt$ around $x=0$ has the form $$f\left ( x \right )={a}_{0}+a_{1}x+a_{2}...
0 votes
0 answers
67
GATE ECE 2018 | Question: 6
Consider $p(s)=s^{3}+ a_{2}s^{2}+a_{1}s+a_{0}$ with all real coefficients. It is known that its derivatives ${p}'(s)$ has no real roots. The number of real roots of $p(s)$ is $0$ $1$ $2$ $3$
Consider $p(s)=s^{3}+ a_{2}s^{2}+a_{1}s+a_{0}$ with all real coefficients. It is known that its derivatives ${p}'(s)$ has no real roots. The number of real roots of $p(s)...
0 votes
0 answers
68
GATE ECE 2017 Set 2 | Question: 30
The minimum value of the function $f(x)=\frac{1}{3} x(x^2-3)$ in the interval $-100≤x≤100$ occurs at $x =$ ________.
The minimum value of the function $f(x)=\frac{1}{3} x(x^2-3)$ in the interval $-100≤x≤100$ occurs at $x =$ ________.
0 votes
0 answers
69
GATE ECE 2017 Set 2 | Question: 26
The values of the integrals $\int_{0}^{1}\left ( \int_{0}^{1}\frac{x-y}{(x+y)^3}dy \right )dx$ and $\int_{0}^{1}\left ( \int_{0}^{1}\frac{x-y}{(x+y)^3}dx \right )dy$ are same and equal to $0.5$ same and equal to $-0.5$ $0.5$ and $-0.5$, respectively $-0.5$ and $0.5$, respectively
The values of the integrals $$\int_{0}^{1}\left ( \int_{0}^{1}\frac{x-y}{(x+y)^3}dy \right )dx$$ and $$\int_{0}^{1}\left ( \int_{0}^{1}\frac{x-y}{(x+y)^3}dx \right )dy$$ ...
Page: