Recent questions and answers in Calculus - GATE CSE Doubts

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TIFR-GS2021 Question
Find the following sum $\frac{1}{2^2 – 1} + \frac{1}{4^2 – 1} + \frac{1}{6^2 – 1} + … + \frac{1}{40^2 – 1}$ (A) $\frac{20}{41}$ (B) $\frac{10}{41}$ (C) $\frac{10}{21}$ (D) $\frac{20}{21}$ (E) $1$

answered Mar 24 in Calculus by ankitgupta.1729 (357 points) | 29 views

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TIRF-GS2021 Question
What is the area of a rectangle with the largest perimeter that can be inscribed in a unit circle (i.e., all the vertices of the rectangle are on the circle with radius 1)? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5

answered Mar 24 in Calculus by ankitgupta.1729 (357 points) | 40 views

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TIFR-GS2021 Question
Consider the sequence $y_n = \frac{1}{\int_{1}^{n}\frac{1}{(1 + x/n)^3}dx}$ for $n = 2, 3, 4, ...$. Which of the following is TRUE? (A) The sequence $\{y_n\}$ does not have a limit as $n\rightarrow \infty$. (B) $y_n\leq 1$ ... $0$. (E) The sequence $\{y_n\}$ first increases and then decreases as $n$ takes values $2, 3, 4, ...$

asked Mar 24 in Calculus by zxy123 (3.6k points) | 3 views

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I have a doubt in engineering mathematics.
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 by einstein (5 points) | 11 views

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#made-easy #limits
1/4 1/8 1/16 none of above ans given is c but according to me it would tends to infinity bcz in numerator n^4 will generate that is asymptotically larger than n3 in denominator. so answer should be d

asked Jan 23 in Calculus by 404 found (37 points) | 16 views

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PREVIOUS YEAR MATHS SELF DOUBT
https://gateoverflow.in/1925/gate2014-1-47 WHY THE B CANT BE ANSWER IF WE DO THE SAME WAY WE DID FOR A AND D? PLEASE SEE...

asked Dec 29, 2020 in Calculus by eyeamgj (29 points) | 14 views

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Applied mathematics by budnick
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 ... on this function is 20<=x<= 50, determine f(20), f(30), f(40), and f(50).

asked Dec 27, 2020 in Calculus by emankamal (5 points) | 18 views

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Calculus testbook question
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 by Dheera (-14 points) | 13 views

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The function f(x)=2.5loge(2+exp(x2−4x+5)) attains a minimum at x=?

asked Nov 26, 2020 in Calculus by neel19 (7 points) | 17 views

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In the interval [0,π] the equation x=cosx has ...

asked Nov 26, 2020 in Calculus by neel19 (7 points) | 22 views

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Calculus doubt
How to draw graph of f(x)= xsinx+cosx with any proper source to understand.

answered Aug 16, 2020 in Calculus by Arkaprava (801 points) | 58 views

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Gatebook:Calculus
The area of triangle is calculated by the formula . If the angle A is measure with 1% error. Find the % error in area. (A) (B) (C) (D)

answered Aug 15, 2020 in Calculus by Arkaprava (801 points) | 35 views

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Gatebook: Calculus
The area enclosed between the parabola and straight line is (A) (B) (C) (D)

answered Aug 15, 2020 in Calculus by Arkaprava (801 points) | 35 views

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Trigonometry
I’m not able to understand my mistake, Please point it out.

answered Aug 12, 2020 in Calculus by Arkaprava (801 points) | 49 views

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self doubt on limits when it tends to infinity
Here , we can’t use L’ Hospital rule since limit is inifinity and what to do with (sinx)^2 ? Please someone explain.

answered Jul 27, 2020 in Calculus by AVICS (145 points) | 34 views

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self doubt on double integration
What to do for y^2 ? Please explain.

asked Jul 26, 2020 in Calculus by Jhaiyam (7 points) | 12 views

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GATE2014-1-47 Video Solution
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 $y$ in ... 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 by admin (573 points) | 12 views

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GATE2015-2-26 Video Solution
Let $f(x)=x^{-\left(\frac{1}{3}\right)}$ and $A$ denote the area of region bounded by $f(x)$ and the X-axis, when $x$ varies from $-1$ to $1$. Which of the following statements is/are TRUE? $f$ is continuous in $[-1, 1]$ $f$ is not bounded in $[-1, 1]$ $A$ is nonzero and finite II only III only II and III only I, II and III

asked Apr 18, 2020 in Calculus by admin (573 points) | 8 views

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GATE2018-16 Video Solution
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 by admin (573 points) | 10 views

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GATE2012-9 Video Solution
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 by admin (573 points) | 11 views

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GATE2014-1-6 Video Solution
Let the function ... exists $\theta \in (\frac{\pi}{6},\frac{\pi}{3})$ such that $f'(\theta)\neq 0$ I only II only Both I and II Neither I Nor II

asked Apr 18, 2020 in Calculus by admin (573 points) | 7 views

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GATE2015-3-9 Video Solution
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 by admin (573 points) | 7 views

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GATE2016-2-02 Video Solution
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 by admin (573 points) | 29 views

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GATE2014-3-6 Video Solution
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 by admin (573 points) | 10 views

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GATE2015-3-45 Video Solution
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 by admin (573 points) | 7 views

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GATE2017-2-10 Video Solution
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 by admin (573 points) | 7 views

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GATE2008-1 Video Solution
$\lim_{x \to \infty}\frac{x-\sin x}{x+\cos x}$ equals $1$ $-1$ $\infty$ $-\infty$

asked Apr 18, 2020 in Calculus by admin (573 points) | 10 views

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GATE2016-1-3 Video Solution
$\lim _{x\rightarrow 4}\frac{\sin(x-4)}{x-4}$=____.

asked Apr 18, 2020 in Calculus by admin (573 points) | 8 views

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GATE2011-31 Video Solution
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 by admin (573 points) | 9 views

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GATE2015-1-44 Video Solution
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 by admin (573 points) | 12 views

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GATE2015-1-4 Video Solution
$\lim_{x\rightarrow \infty } x^{ \tfrac{1}{x}}$ is $\infty $ 0 1 Not defined

asked Apr 18, 2020 in Calculus by admin (573 points) | 7 views

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GATE2017-1-28 Video Solution
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 by admin (573 points) | 5 views

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GATE2008-25 Video Solution
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 by admin (573 points) | 8 views

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GATE2014-3-47 Video Solution
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 by admin (573 points) | 7 views

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GATE2013-22 Video Solution
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 $ ... $} \end{cases}$ $f(x) = \begin{cases} \frac{1}{x^3-27}&\text{if $x \neq 3$ } \end{cases}$

asked Apr 18, 2020 in Calculus by admin (573 points) | 8 views

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GATE2010-5 Video Solution
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 by admin (573 points) | 6 views

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GATE2008-IT-31 Video Solution
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 by admin (573 points) | 12 views

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GATE2019-13 Video Solution
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 by admin (573 points) | 8 views

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GATE2000-2.3 Video Solution
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 by admin (573 points) | 8 views

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GATE2015-2-GA-3 Video Solution
Consider a function $f(x) = 1- |x| \text{ on } -1 \leq x \leq 1$. The value of $x$ at which the function attains a maximum, and the maximum value of the function are: $0, -1$ $-1, 0$ $0, 1$ $-1, 2$

asked Apr 18, 2020 in Calculus by admin (573 points) | 9 views

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Recent questions and answers in Calculus

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