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Welcome to GATE CSE Doubts, where you can ask questions and receive answers from other members of the community.

Recent questions tagged calculus

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2 answers 15 views
Hi I need other resource for calculus cause I doing now mitocw David jerison calculus course as I on 10th video I realized this course is way too far for gate exam or psu exams cause this course give detailed proof and solution for every formula for differentiation like ... can follow kreatyrx? Please help me I am very confused ? As I give this week to complete engg maths full please reply fast
asked 6 days ago in Mathematical Logic ykrishnay 103 points 15 views
0 votes
1 answer 10 views
i study calculus but now i totally confused in calculus cause what is the exact syllabus of calculus for gate cse in integration , so all types of integration i do like multiple integration etc ? please reply as i stuck in between.
asked Jul 22 in Mathematical Logic ykrishnay 103 points 10 views
0 votes
1 answer 161 views
linear-algebra .. 1. https://gateoverflow.in/questions/mathematics/linear-algebra 2. https://gatecse.in/linear-algebra/ 3. https://gateoverflow.in/tag/determinants 4. https://gateoverflow.in/tag/system-of-equations 5. https://gateoverflow.in/tag/system-of-equations? ... . Finding values by Mean Value Theorem. Integration.... https://drive.google.com/file/d/0Byt7-j-JD0d0bmxlRkZGcjN2cjA/view .....
asked Jul 20 in GATE asqwer 633 points 161 views
1 vote
1 answer 15 views
The value of $\int_{0}^{inf}$ $e^{-y^{3}}.y^{1/2} dy$ is ? Ans = $\sqrt{\Pi } * 1/3$ How ?
asked Jun 30 in Calculus 10nikhilsharma01 9 points 15 views
0 votes
1 answer 38 views
hi so what is least resource for calculus mainly for gate only, cause mit video is very long it is very time consuming
asked Jun 28 in Mathematical Logic ykrishnay 103 points 38 views
0 votes
0 answers 18 views
despite knowing different numerical methods like taylor’s series , R K Method , Eulers method , which one to choose based on the matrix pattern.
asked Mar 2 in Calculus einstein 5 points 18 views
2 votes
2 answers 534 views
Suppose that $f: \mathbb{R} \rightarrow \mathbb{R}$ is a continuous function on the interval $[-3, 3]$ and a differentiable function in the interval $(-3,3)$ such that for every $x$ in the interval, $f’(x) \leq 2$. If $f(-3)=7$, then $f(3)$ is at most __________
asked Feb 18 in Calculus Arjun 1.5k points 534 views
0 votes
2 answers 540 views
Consider the following expression.$\displaystyle \lim_{x\rightarrow-3}\frac{\sqrt{2x+22}-4}{x+3}$The value of the above expression (rounded to 2 decimal places) is ___________.
asked Feb 18 in Calculus Arjun 1.5k points 540 views
0 votes
0 answers 21 views
Marriage Prospects Data released by the Census Bureau in 1986 indicated the likelihood that never-married women would eventually marry. The data indicated that the older the woman, the less the likelihood of marriage. Specifically, two statistics indicated that women who were 45 and never-married had an ... restricted domain on this function is 20<=x<= 50, determine f(20), f(30), f(40), and f(50).
asked Dec 27, 2020 in Calculus emankamal 5 points 21 views
0 votes
0 answers 17 views
Consider a function f(y) = $y^3 - 7y^2 + 5$ given on interval [p,q]. If f(y) satisfies hypothesis of Rolle’s theorem and p=0 then what is the value of q? The answer given was 7
asked Dec 10, 2020 in Calculus Dheera -14 points 17 views
0 votes
0 answers 20 views
TIFR 2010 question. For finding the minimum, we have to find the first derivative of the fun. The fun seems complex and I don’t know how to derive it.
asked Nov 26, 2020 in Calculus neel19 7 points 20 views
0 votes
0 answers 17 views
Let $f$ be a twice differentiable function such that \[ f^{‘’}(x)=-f(x) ; f(x)=g(x) \text { and } h(x)=f^{2}(x)+g^{2}(x) \] Given that $h(5)=11,$ find $h(10)$
asked May 23, 2020 in Others Amartya 5 points 17 views
0 votes
0 answers 17 views
A function $f(x)$ is continuous in the interval $[0,2]$. It is known that $f(0) = f(2) = -1$ and $f(1) = 1$. Which one of the following statements must be true? There exists a $y$ in the interval $(0,1)$ such that $f(y) = f(y+1)$ For every $y$ ... maximum value of the function in the interval $(0,2)$ is $1$ There exists a $y$ in the interval $(0,1)$ such that $f(y)$ = $-f(2-y)$
asked Apr 18, 2020 in Calculus admin 573 points 17 views
0 votes
0 answers 19 views
The number of roots of $e^{x}+0.5x^{2}-2=0$ in the range $[-5,5]$ is $0$ $1$ $2$ $3$
asked Apr 18, 2020 in Numerical Ability admin 573 points 19 views
0 votes
0 answers 14 views
The value of $\int^{\pi/4} _0 x \cos(x^2) dx$ correct to three decimal places (assuming that $\pi = 3.14$) is ____
asked Apr 18, 2020 in Calculus admin 573 points 14 views
0 votes
0 answers 19 views
Consider the function $f(x) = \sin(x)$ in the interval $x =\left[\frac{\pi}{4},\frac{7\pi}{4}\right]$. The number and location(s) of the local 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 $\dfrac{3\pi}{2}$
asked Apr 18, 2020 in Calculus admin 573 points 19 views
0 votes
0 answers 12 views
Let the function $f(\theta) = \begin{vmatrix} \sin\theta & \cos\theta & \tan\theta \\ \sin(\frac{\pi}{6}) & \cos(\frac{\pi}{6}) & \tan(\frac{\pi}{6}) & \\ \sin(\frac{\pi}{3}) & \cos(\frac{\pi}{3}) & \tan(\frac{\pi}{3}) \end{vmatrix} $ ... $\theta \in (\frac{\pi}{6},\frac{\pi}{3})$ such that $f'(\theta)\neq 0$ I only II only Both I and II Neither I Nor II
asked Apr 18, 2020 in Calculus admin 573 points 12 views
0 votes
0 answers 14 views
The value of $\lim_{x \rightarrow \infty} (1+x^2)^{e^{-x}}$ is $0$ $\frac{1}{2}$ $1$ $\infty$
asked Apr 18, 2020 in Calculus admin 573 points 14 views
0 votes
0 answers 36 views
Let $f(x)$ be a polynomial and $g(x)=f'(x)$ be its derivative. If the degree of $(f(x)+f(-x))$ is $10$, then the degree of $(g(x) - g(-x))$ is __________.
asked Apr 18, 2020 in Calculus admin 573 points 36 views
0 votes
0 answers 15 views
If $\int \limits_0^{2 \pi} |x \: \sin x| dx=k\pi$, then the value of $k$ is equal to ______.
asked Apr 18, 2020 in Calculus admin 573 points 15 views
0 votes
0 answers 12 views
If for non-zero $x, \: af(x) + bf(\frac{1}{x}) = \frac{1}{x} - 25$ where a $a \neq b \text{ then } \int_1^2 f(x)dx$ is $\frac{1}{a^2 - b^2} \begin{bmatrix} a(\ln 2 - 25) + \frac{47b}{2} \end{bmatrix}$ ... $\frac{1}{a^2 - b^2} \begin{bmatrix} a(\ln 2 - 25) - \frac{47b}{2} \end{bmatrix}$
asked Apr 18, 2020 in Calculus admin 573 points 12 views
0 votes
0 answers 11 views
If $f(x) = R \: \sin ( \frac{\pi x}{2}) + S, f’\left(\frac{1}{2}\right) = \sqrt{2}$ and $\int_0^1 f(x) dx = \frac{2R}{\pi}$, then the constants $R$ and $S$ are $\frac{2}{\pi}$ and $\frac{16}{\pi}$ $\frac{2}{\pi}$ and 0 $\frac{4}{\pi}$ and 0 $\frac{4}{\pi}$ and $\frac{16}{\pi}$
asked Apr 18, 2020 in Calculus admin 573 points 11 views
0 votes
0 answers 13 views
$\lim_{x \to \infty}\frac{x-\sin x}{x+\cos x}$ equals $1$ $-1$ $\infty$ $-\infty$
asked Apr 18, 2020 in Calculus admin 573 points 13 views
0 votes
0 answers 12 views
$\lim _{x\rightarrow 4}\frac{\sin(x-4)}{x-4}$=____.
asked Apr 18, 2020 in Calculus admin 573 points 12 views
0 votes
0 answers 13 views
Given $i = \sqrt{-1}$, what will be the evaluation of the definite integral $\int \limits_0^{\pi/2} \dfrac{\cos x +i \sin x} {\cos x - i \sin x} dx$ ? $0$ $2$ $-i$ $i$
asked Apr 18, 2020 in Calculus admin 573 points 13 views
0 votes
0 answers 15 views
Compute the value of: $\large \int_{\frac{1}{\pi}}^{\frac{2}{\pi}}\frac{\cos(1/x)}{x^{2}}dx$
asked Apr 18, 2020 in Calculus admin 573 points 15 views
0 votes
0 answers 12 views
$\lim_{x\rightarrow \infty } x^{ \tfrac{1}{x}}$ is $\infty $ 0 1 Not defined
asked Apr 18, 2020 in Calculus admin 573 points 12 views
0 votes
0 answers 8 views
The value of $\lim_{x\rightarrow 1} \frac{x^{7}-2x^{5}+1}{x^{3}-3x^{2}+2}$ is $0$ is $-1$ is $1$ does not exist
asked Apr 18, 2020 in Calculus admin 573 points 8 views
0 votes
0 answers 11 views
A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve $3x^4-16x^3+24x^2+37$ is $0$ $1$ $2$ $3$
asked Apr 18, 2020 in Calculus admin 573 points 11 views
0 votes
0 answers 10 views
The value of the integral given below is $\int \limits_0^{\pi} \: x^2 \: \cos x\:dx$ $-2\pi$ $\pi$ $-\pi$ $2\pi$
asked Apr 18, 2020 in Calculus admin 573 points 10 views
0 votes
0 answers 12 views
Which one of the following functions is continuous at $x = 3?$ $f(x) = \begin{cases} 2,&\text{if $x = 3$ } \\ x-1& \text{if $x > 3$}\\ \frac{x+3}{3}&\text{if $x < 3$ } \end{cases}$ $f(x) = \begin{cases} 4,&\text{if $x = 3$ } \\ 8-x& \text{if $x \neq 3$} \end{cases}$ ... $ } \\ x-4& \text{if $x > 3$} \end{cases}$ $f(x) = \begin{cases} \frac{1}{x^3-27}&\text{if $x \neq 3$ } \end{cases}$
asked Apr 18, 2020 in Calculus admin 573 points 12 views
0 votes
0 answers 9 views
What is the value of $\lim_{n \to \infty}\left(1 - \frac{1}{n}\right)^{2n}$ ? 0 $e^{-2}$ $e^{-1/2}$ 1
asked Apr 18, 2020 in Calculus admin 573 points 9 views
0 votes
0 answers 18 views
If $f(x)$ is defined as follows, what is the minimum value of $f(x)$ for $x \in (0, 2]$ ? $f(x) = \begin{cases} \frac{25}{8x} \text{ when } x \leq \frac{3}{2} \\ x+ \frac{1}{x} \text { otherwise}\end{cases}$ $2$ $2 \frac{1}{12}$ $2\frac{1}{6}$ $2\frac{1}{2}$
asked Apr 18, 2020 in Calculus admin 573 points 18 views
0 votes
0 answers 13 views
Compute $\displaystyle \lim_{x \rightarrow 3} \frac{x^4-81}{2x^2-5x-3}$ $1$ $53/12$ $108/7$ Limit does not exist
asked Apr 18, 2020 in Calculus admin 573 points 13 views
0 votes
0 answers 13 views
Let $S = \sum_{i=3}^{100} i \log_{2} i$, and $T = \int_{2}^{100} x \log_{2}x dx$. Which of the following statements is true? $S > T$ $S = T$ $S < T$ and $2S > T$ $2S ≤ T$
asked Apr 18, 2020 in Calculus admin 573 points 13 views
0 votes
0 answers 13 views
What is the maximum value of the function $f(x) = 2x^2 - 2x + 6$ in the interval $\left[0,2 \right]$? 6 10 12 5.5
asked Apr 18, 2020 in Calculus admin 573 points 13 views
0 votes
0 answers 13 views
The formula used to compute an approximation for the second derivative of a function $f$ at a point $X_0$ is $\dfrac{f(x_0 +h) + f(x_0 – h)}{2}$ $\dfrac{f(x_0 +h) - f(x_0 – h)}{2h}$ $\dfrac{f(x_0 +h) + 2f(x_0) + f(x_0 – h)}{h^2}$ $\dfrac{f(x_0 +h) - 2f(x_0) + f(x_0 – h)}{h^2}$
asked Apr 18, 2020 in Calculus admin 573 points 13 views
0 votes
0 answers 19 views
What is the value of $\int_{0}^{2\pi}(x-\pi)^2 (\sin x) dx$ $-1$ $0$ $1$ $\pi$
asked Apr 18, 2020 in Calculus admin 573 points 19 views
0 votes
0 answers 14 views
Consider the following two statements about the function $f(x)=\left\vert x\right\vert$: P. $f(x)$ is continuous for all real values of $x$. Q. $f(x)$ is differentiable for all real values of $x$ . Which of the following is TRUE? $P$ is true and $Q$ is false. $P$ is false and $Q$ is true. Both $P$ and $Q$ are true. Both $P$ and $Q$ are false.
asked Apr 18, 2020 in Calculus admin 573 points 14 views
0 votes
0 answers 10 views
$\int^{\pi/4}_0 (1-\tan x)/(1+\tan x)\,dx $ $0$ $1$ $ln 2$ $1/2 ln 2$
asked Apr 18, 2020 in Calculus admin 573 points 10 views
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