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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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Highest voted questions in Calculus

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581
Calculus
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582
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 )=$$\int_{-2}^{2}x^{-\frac{2}{7}}dx$Is this function f(x) is continuous, bounded and differentiable?(In exam hall is it possible to draw the graph for ...
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586
Integration
Evaluate $\Large\int_3^7 \sqrt[4]{(x-3)(7-x)} dx$
Evaluate $\Large\int_3^7 \sqrt[4]{(x-3)(7-x)} dx$
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587
Multiple integration
Evaluate $\Large\int_1^4\Large\int_\sqrt{y}^2(x^{2}+y^{2})dA $ by changing the order of integration
Evaluate $\Large\int_1^4\Large\int_\sqrt{y}^2(x^{2}+y^{2})dA $ by changing the order of integration
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3 answers
588
Integration
$\int \left ( \sin\theta \right )^{\frac{1}{2}}d\theta$
$\int \left ( \sin\theta \right )^{\frac{1}{2}}d\theta$
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589
ISI2017-MMA-25
For $a,b \in \mathbb{R}$ and $b > a$ , the maximum possible value of the integral $\int_{a}^{b}(7x-x^{2}-10)dx$ is $\frac{7}{2}\\$ $\frac{9}{2}\\$ $\frac{11}{2}\\$ none of these
For $a,b \in \mathbb{R}$ and $b a$ , the maximum possible value of the integral $\int_{a}^{b}(7x-x^{2}-10)dx$ is$\frac{7}{2}\\$$\frac{9}{2}\\$$\frac{11}{2}\\$none of the...
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590
Calculus Integration
$I=\int_{3}^{7}((x-3)(7-x))^{\frac{1}{4}}dx$
$I=\int_{3}^{7}((x-3)(7-x))^{\frac{1}{4}}dx$
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592
General Math
What is value of $\log _{2}10$? In general calculator $\ln _{2}10$ is giving 2.3.... But it should be 3. something right?
What is value of $\log _{2}10$?In general calculator $\ln _{2}10$ is giving 2.3....But it should be 3. somethingright?
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2 answers
593
definite integration
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1 answer
594
Maths calculus
a)π/√2 B) √π/2 C) π/2 D)√(π/2
a)π/√2 B) √π/2C) π/2 D)√(π/2
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595
Maths calculus
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596
Maths calculus
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597
Problems in Calculus Of One Variable by I.A. Maron
Prove that 0.101001000...1000....01 is irrational. can i get the exact solution.
Prove that 0.101001000...1000....01 is irrational.can i get the exact solution.
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598
ISI-2016-05
Let $f(x,y) = \begin{cases} \dfrac{x^2y}{x^4+y^2}, & \text{ if } (x,y) \neq (0,0) \\ 0 & \text{ if } (x,y) = (0,0)\end{cases}$ Then $\displaystyle{\lim_{(x,y)\rightarrow(0,0)}}f (x,y)$ equals $0$ equals $1$ equals $2$ does not exist
Let $$f(x,y) = \begin{cases} \dfrac{x^2y}{x^4+y^2}, & \text{ if } (x,y) \neq (0,0) \\ 0 & \text{ if } (x,y) = (0,0)\end{cases}$$Then $\displaystyle{\lim_{(x,y)...
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600
Mathematics GATE 2018 EE: 43
Let $f(x) = 3x^{3} - 7x^{2} + 5x + 6$. The maximum value of $f(x)$ over the the interval $[ 0 , 2 ]$ is_________(Upto $1$ decimal place)
Let $f(x) = 3x^{3} - 7x^{2} + 5x + 6$. The maximum value of $f(x)$ over the the interval $[ 0 , 2 ]$ is_________(Upto $1$ decimal place)
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