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

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2024-1} &\textbf{2024-2} &\textbf{2023} &\textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} &1&1&2& 1 &1&1&1&1.16&2
\\\hline\textbf{2 Marks Count} &0&0&0& 0 &0&0&0&0&0
\\\hline\textbf{Total Marks} & 1&1&2&1 &1&1&\bf{1}&\bf{1.16}&\bf{2}\\\hline
\end{array}}}$$

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Recent questions in Calculus

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211
ME TEST SERIES
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212
Integration
How to solve it?
How to solve it?
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1 answer
213
UPPCL AE 2018:81
The value of $\dfrac{|x|}{x}$ at $x= 0$ is: Infinity Not defined $1$ $0$
The value of $\dfrac{|x|}{x}$ at $x= 0$ is:InfinityNot defined$1$$0$
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214
self doubt
$\lim_{x\rightarrow \frac{\pi }{2}}cosx^{cosx}$ can we straight away say $0^{0}=0$ ?
$\lim_{x\rightarrow \frac{\pi }{2}}cosx^{cosx}$can we straight away say $0^{0}=0$ ?
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215
calculus question
Question Number 4?
Question Number 4?
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216
#integration
I=$\int_{1}^{\infty }a^{-ceil (log _{b} x ) } dx$
I=$\int_{1}^{\infty }a^{-ceil (log _{b} x ) } dx$
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217
#integration
$I=\int sin(2x) cos(3x) dx$ 1.(5cosx-cos5x)/10 2.(5sinx-sin5x)/10 3.both 4.none
$I=\int sin(2x) cos(3x) dx$1.(5cosx-cos5x)/102.(5sinx-sin5x)/103.both4.none
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218
Math doubt
Is it true $\frac{1}{1+x^{2}}=1-x^{2}$ Is it applied every function? (like limit func, generating func)?
Is it true$\frac{1}{1+x^{2}}=1-x^{2}$Is it applied every function? (like limit func, generating func)?
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219
Clarification on Topic
In the syllabus it was said “differentiability” does this mean we have partial differentiation.??
In the syllabus it was said “differentiability” does this mean we have partial differentiation.??
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1 votes
2 answers
220
GATE Overflow | Mock GATE | Test 1 | Question: 19
Evaluate the limit: $ \lim_{x \to -3} \frac{\sqrt{2x+22}-4}{x+3}$ $\frac{1}{2}$ $\frac{1}{4}$ $\frac{1}{8}$ $\frac{1}{16}$
Evaluate the limit:$$ \lim_{x \to -3} \frac{\sqrt{2x+22}-4}{x+3}$$$\frac{1}{2}$$\frac{1}{4}$$\frac{1}{8}$$\frac{1}{16}$
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221
Integration
If n is a positive integer, then $\int_{0}^{\pi} \frac{sin(2nx)}{sinx} dx$
If n is a positive integer, then $$\int_{0}^{\pi} \frac{sin(2nx)}{sinx} dx$$
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222
Shortcut Method to find Maxima and Minima in Calculus
https://www.youtube.com/watch?v=tyiQLindzCE This is a great video but covers formula for cubic root what about for any given equation x^n,what would be the solution?
https://www.youtube.com/watch?v=tyiQLindzCEThis is a great video but covers formula for cubic root what about for any given equation x^n,what would be the solution?
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223
self doubt
How to solve these questions $(1)$ $I=\int_{0}^{1}(xlogx)^{4}dx$ $(2)$ $I=\frac{1}{\sqrt{2\pi}}\int_{0}^{\infty}e^{\frac{-x^{2}}{8}}dx$ $(3)$ $I=\int_{0}^{\infty}x^{\frac{1}{4}}.e^{-\sqrt{x}}dx$
How to solve these questions$(1)$ $I=\int_{0}^{1}(xlogx)^{4}dx$$(2)$ $I=\frac{1}{\sqrt{2\pi}}\int_{0}^{\infty}e^{\frac{-x^{2}}{8}}dx$$(3)$ $I=\int_{0}^{\infty}x^{\frac{...
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7 votes
2 answers
224
TIFR CSE 2019 | Part A | Question: 13
Consider the integral $\int^{1}_{0} \frac{x^{300}}{1+x^2+x^3} dx$ What is the value of this integral correct up to two decimal places? $0.00$ $0.02$ $0.10$ $0.33$ $1.00$
Consider the integral$$\int^{1}_{0} \frac{x^{300}}{1+x^2+x^3} dx$$What is the value of this integral correct up to two decimal places?$0.00$$0.02$$0.10$$0.33$$1.00$
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226
#maths #limit
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227
aai 2018
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228
GATE 2016 MA Limits
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229
GATE 2016 MA Calculus
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230
GATE 2013 MA Calculus
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