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Syllabus: Limits, Continuity, and Differentiability, Maxima and minima, Mean value theorem, Integration.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 1 &1&1&1&1&1&0&1&1&1&0&0.9&1
\\\hline\textbf{2 Marks Count} & 0 &0&0&0&0&0&1&0&0&0&0&0.1&1
\\\hline\textbf{Total Marks} & 1 &1&1&1&1&1&2&1&1&1&\bf{1}&\bf{1.1}&\bf{2}\\\hline
\end{array}}}$$

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Hot questions in Calculus

1 votes
2 answers
361
Integration- CE 2013
Find the value of the integral $\int_{0}^{\pi/6}cos^43\theta\ sin^36\theta\ d\theta$ Please show the steps.(upload a pic of your solution) a) 0 b) 1/15 c) 8/3 d) 1
Find the value of the integral $$\int_{0}^{\pi/6}cos^43\theta\ sin^36\theta\ d\theta$$Please show the steps.(upload a pic of your solution)a) 0b) 1/15c) 8/3d) 1
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0 votes
0 answers
362
ISI2016-MMA-7
The set of value(s) of $\alpha$ for which $y(t)=t^{\alpha}$ is a solution to the differential equation $t^2 \frac{d^2y}{dx^2}-2t \frac{dy}{dx}+2y =0 \: \text{ for } t>0$ is $\{1\}$ $\{1, -1\}$ $\{1, 2\}$ $\{-1, 2\}$
The set of value(s) of $\alpha$ for which $y(t)=t^{\alpha}$ is a solution to the differential equation $$t^2 \frac{d^2y}{dx^2}-2t \frac{dy}{dx}+2y =0 \: \text{ for } t>0$...
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0 votes
0 answers
363
limit
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0 votes
0 answers
364
What is sum of the sequence?
What is sum of the series 1+ √2+ √3 +√4.....+√n ? Assymptotic answer will be okay too.
What is sum of the series1+ √2+ √3 +√4.....+√n ?Assymptotic answer will be okay too.
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0 votes
0 answers
366
Find sequence's sum?
What is sum of the following series 1+ √2+ √3 +√4.....+√n ? Asymptotic answer will be okay too.
What is sum of the following series1+ √2+ √3 +√4.....+√n ?Asymptotic answer will be okay too.
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10 votes
2 answers
367
TIFR CSE 2011 | Part A | Question: 4
Consider the problem of maximizing $x^{2}-2x+5$ such that $0< x< 2$. The value of $x$ at which the maximum is achieved is: $0.5$ $1$ $1.5$ $1.75$ None of the above
Consider the problem of maximizing $x^{2}-2x+5$ such that $0< x< 2$. The value of $x$ at which the maximum is achieved is:$0.5$$1$$1.5$$1.75$None of the above
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0 votes
1 answer
368
Calculus-Self Doubt
Is the function $f(x)=\frac{1}{x^{\frac{1}{3}}}$ continous in the interval [-1 0) ?
Is the function $f(x)=\frac{1}{x^{\frac{1}{3}}}$ continous in the interval [-1 0) ?
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0 votes
1 answer
369
lt x→0(3cosx+2sin3x)^(1/x)
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0 votes
0 answers
372
Integration
$f\left ( x \right )=$\int_{-2}^{2}x^{-\frac{2}{7}}dx$ Is this function f(x) is continuous, bounded and differentiable? (In exam hall is it possible to draw the graph for this function f(x), or some other procedure to follow to ans this)
$f\left ( x \right )=$$\int_{-2}^{2}x^{-\frac{2}{7}}dx$Is this function f(x) is continuous, bounded and differentiable?(In exam hall is it possible to draw the graph for ...
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1 votes
1 answer
373
MadeEasy Test Series: Calculus - Functions
Consider the following function $f(x)=\frac{x}{2x+1} , \, x\not= -\frac{1}{2}$ ... is defined on $R \rightarrow R-\{ \frac{1}{2} \}$, then it will be a bijection. Please let me know what's correct?
Consider the following function$f(x)=\frac{x}{2x+1} , \, x\not= -\frac{1}{2}$Is the function a bijection?Yes, this is a one-to-one function.For onto, let's suppose functi...
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10 votes
4 answers
374
GATE CSE 1997 | Question: 4.1
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
What is the maximum value of the function $f(x) = 2x^2 - 2x + 6$ in the interval $\left[0,2 \right]$?610125.5
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2 votes
2 answers
375
Limit
Is answer will be 1 or 5? $\lim_{x\rightarrow \alpha }\left ( \frac{x+6}{x+1} \right )^{x+4}$
Is answer will be 1 or 5?$\lim_{x\rightarrow \alpha }\left ( \frac{x+6}{x+1} \right )^{x+4}$
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1 votes
1 answer
376
Definite Integral
$\displaystyle S = \int_{0}^{2\pi } \sqrt{4\cos^{2}t +\sin^{2}t} \, \, dt$ Please explain how to solve it.
$\displaystyle S = \int_{0}^{2\pi } \sqrt{4\cos^{2}t +\sin^{2}t} \, \, dt$Please explain how to solve it.
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0 votes
2 answers
377
SELF DOUBT
0/infinity is determinent form or inderminent form while solving limits
0/infinity is determinent form or inderminent form while solving limits
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7 votes
1 answer
378
ISI-2017 MMA
Let $S \subseteq R$. Consider the statement: "There exists a continuous function $f:S \rightarrow S$ such that $f(x) \neq x$ for all $x$ belongs to $S$." This statement is false if $S$ equals $[2,3]$ $[2,3]$ $[-3,-2] \cup [2,3]$ $(-\infty \text{ to} +\infty)$
Let $S \subseteq R$. Consider the statement:"There exists a continuous function $f:S \rightarrow S$ such that $f(x) \neq x$ for all $x$ belongs to $S$."This statement is ...
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15 votes
6 answers
379
TIFR CSE 2010 | Part A | Question: 7
The limit of $\dfrac{10^{n}}{n!}$ as $n \to \infty$ is. $0$ $1$ $e$ $10$ $\infty$
The limit of $\dfrac{10^{n}}{n!}$ as $n \to \infty$ is.$0$$1$$e$$10$$\infty$
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0 votes
0 answers
380
ISI2017-MMA-25
For $a,b \in \mathbb{R}$ and $b > a$ , the maximum possible value of the integral $\int_{a}^{b}(7x-x^{2}-10)dx$ is $\frac{7}{2}\\$ $\frac{9}{2}\\$ $\frac{11}{2}\\$ none of these
For $a,b \in \mathbb{R}$ and $b a$ , the maximum possible value of the integral $\int_{a}^{b}(7x-x^{2}-10)dx$ is$\frac{7}{2}\\$$\frac{9}{2}\\$$\frac{11}{2}\\$none of the...
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