# Recent questions tagged calculus

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
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.
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 .....
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The value of $\int_{0}^{inf}$ $e^{-y^{3}}.y^{1/2} dy$ is ? Ans = $\sqrt{\Pi } * 1/3$ How ?
hi so what is least resource for calculus mainly for gate only, cause mit video is very long it is very time consuming
despite knowing different numerical methods like taylor’s series , R K Method , Eulers method , which one to choose based on the matrix pattern.
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 __________
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 ___________.
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).
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
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.
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 $h(10)$
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 $f(y)$ = $-f(2-y)$
The number of roots of $e^{x}+0.5x^{2}-2=0$ in the range $[-5,5]$ is $0$ $1$ $2$ $3$
The value of $\int^{\pi/4} _0 x \cos(x^2) dx$ correct to three decimal places (assuming that $\pi = 3.14$) is ____
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 $\dfrac{3\pi}{2}$
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
The value of $\lim_{x \rightarrow \infty} (1+x^2)^{e^{-x}}$ is $0$ $\frac{1}{2}$ $1$ $\infty$
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 __________.
If $\int \limits_0^{2 \pi} |x \: \sin x| dx=k\pi$, then the value of $k$ is equal to ______.
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 $\frac{1}{a^2 - b^2} \begin{bmatrix} a(\ln 2 - 25) + \frac{47b}{2} \end{bmatrix}$ ... $\frac{1}{a^2 - b^2} \begin{bmatrix} a(\ln 2 - 25) - \frac{47b}{2} \end{bmatrix}$
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 $\frac{16}{\pi}$
$\lim_{x \to \infty}\frac{x-\sin x}{x+\cos x}$ equals $1$ $-1$ $\infty$ $-\infty$
$\lim _{x\rightarrow 4}\frac{\sin(x-4)}{x-4}$=____.
Given $i = \sqrt{-1}$, what will be the evaluation of the definite integral $\int \limits_0^{\pi/2} \dfrac{\cos x +i \sin x} {\cos x - i \sin x} dx$ ? $0$ $2$ $-i$ $i$
Compute the value of: $\large \int_{\frac{1}{\pi}}^{\frac{2}{\pi}}\frac{\cos(1/x)}{x^{2}}dx$
$\lim_{x\rightarrow \infty } x^{ \tfrac{1}{x}}$ is $\infty$ 0 1 Not defined
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
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 $0$ $1$ $2$ $3$
The value of the integral given below is $\int \limits_0^{\pi} \: x^2 \: \cos x\:dx$ $-2\pi$ $\pi$ $-\pi$ $2\pi$
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$} \end{cases}$
What is the value of $\lim_{n \to \infty}\left(1 - \frac{1}{n}\right)^{2n}$ ? 0 $e^{-2}$ $e^{-1/2}$ 1
If $f(x)$ is defined as follows, what is the minimum value of $f(x)$ for $x \in (0, 2]$ ? $f(x) = \begin{cases} \frac{25}{8x} \text{ when } x \leq \frac{3}{2} \\ x+ \frac{1}{x} \text { otherwise}\end{cases}$ $2$ $2 \frac{1}{12}$ $2\frac{1}{6}$ $2\frac{1}{2}$
Compute $\displaystyle \lim_{x \rightarrow 3} \frac{x^4-81}{2x^2-5x-3}$ $1$ $53/12$ $108/7$ Limit does not exist
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 $2S > T$ $2S ≤ T$
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
The formula used to compute an approximation for the second derivative of a function $f$ at a point $X_0$ is $\dfrac{f(x_0 +h) + f(x_0 – h)}{2}$ $\dfrac{f(x_0 +h) - f(x_0 – h)}{2h}$ $\dfrac{f(x_0 +h) + 2f(x_0) + f(x_0 – h)}{h^2}$ $\dfrac{f(x_0 +h) - 2f(x_0) + f(x_0 – h)}{h^2}$
What is the value of $\int_{0}^{2\pi}(x-\pi)^2 (\sin x) dx$ $-1$ $0$ $1$ $\pi$
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.
$\int^{\pi/4}_0 (1-\tan x)/(1+\tan x)\,dx$ $0$ $1$ $ln 2$ $1/2 ln 2$