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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

3 votes
1 answer
572
Gate_EE_2006
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0 votes
1 answer
573
Lagrange 's Mean Value Theorem
Question: The value of $\zeta$ of $f(b) - f(a) = (b-a) \cdot f'(\zeta)$ for the function $f(x) = Ax^2 + Bx +C$ in the interval $[a,b]$ is _______ My Attempt : STEP 1: $f(x)$ is polynomial function therefore continuous STEP 2: $f(x)$ is ... How to proceed further?
Question:The value of $\zeta$ of $f(b) - f(a) = (b-a) \cdot f'(\zeta)$ for the function $f(x) = Ax^2 + Bx +C$ in the interval $[a,b]$ is _______My Attempt :STEP 1: $f(x)...
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7 votes
3 answers
574
TIFR CSE 2012 | Part A | Question: 14
The limit $\displaystyle \lim_{n \rightarrow \infty} \left(\sqrt{n^{2}+n}-n\right)$ equals. $\infty$ $1$ $1 / 2$ $0$ None of the above
The limit $\displaystyle \lim_{n \rightarrow \infty} \left(\sqrt{n^{2}+n}-n\right)$ equals.$\infty$$1$$1 / 2$$0$None of the above
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1 votes
1 answer
575
Continuity
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2 votes
1 answer
576
Limit
Calculate the limit $\lim_{x \rightarrow 1-} \sqrt[3]{x+1} \: ln \: (x+1)$ 1 0 2 Does not exist
Calculate the limit$\lim_{x \rightarrow 1-} \sqrt[3]{x+1} \: ln \: (x+1)$102Does not exist
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0 votes
1 answer
577
TEST SERIES
Plz give solution
Plz give solution
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0 votes
0 answers
578
calculus differentiation question
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0 votes
1 answer
579
What is the difficulty level of Calculus questions?
I find Calculus part very difficult, what is the difficulty level of Calculus? also please let me know which part should I focus in Mathematic.
I find Calculus part very difficult, what is the difficulty level of Calculus? also please let me know which part should I focus in Mathematic.
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3 votes
2 answers
580
Calculus
Can anyone tell me range of f(x)=|sinx|+|cosx|
Can anyone tell me range of f(x)=|sinx|+|cosx|
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3 votes
1 answer
581
TIFR-2015-Maths-A-8
Let $f(x)=\frac{e^{\frac{-1}{x}}}{x}$, where $x \in (0, 1)$. Then on $(0, 1)$. $f$ is uniformly continuous. $f$ is continuous but not uniformly continuous. $f$ is unbounded. $f$ is not continuous.
Let $f(x)=\frac{e^{\frac{-1}{x}}}{x}$, where $x \in (0, 1)$. Then on $(0, 1)$.$f$ is uniformly continuous.$f$ is continuous but not uniformly continuous.$f$ is unbounded....
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0 votes
3 answers
583
Limit
Can we calculate. $\textstyle \lim_{n \to \infty}\frac{2^{n}}{3^{n}}$ if yes then what is the value.
Can we calculate. $\textstyle \lim_{n \to \infty}\frac{2^{n}}{3^{n}}$ if yes then what is the value.
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0 votes
1 answer
584
Calcus
1. f(x)=|x|+ |x+1|+ |x+2| is diffrentiable at x= 1 How it 1 Please Explain ?
1. f(x)=|x|+ |x+1|+ |x+2| is diffrentiable at x= 1 How it 1 Please Explain ?
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1 votes
1 answer
585
limits
Let $f(x,y) = \begin{cases} 1, & \quad if \: xy=0, \\ xy, & \quad xy \neq 0. \end{cases}$ Then $f$ is continuous at $(0,0)$ and $\frac{\partial f}{ \partial x} (0,0)$ exists $f$ is not continuous at $(0,0)$ ... $f$ is not continuous at $(0,0)$ and $\frac{\partial f}{ \partial x} (0,0)$ does not exist
Let $f(x,y) = \begin{cases} 1, & \quad if \: xy=0, \\ xy, & \quad xy \neq 0. \end{cases}$Then$f$ is continuous at $(0,0)$ and $\frac{\partial f}{ \partial x} (0,0)$ exist...
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0 votes
1 answer
586
limits
$\lim_{x \to 0}x\log _x a$ $(A)0$ $(B)\log_ae$ $(C)1$ $(D)\log a$
$\lim_{x \to 0}x\log _x a$$(A)0$ $(B)\log_ae$$(C)1$ ...
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2 votes
2 answers
588
Solve
At $t=0$, the function $f(t)=\frac{\sin t}{t}$ has (A) a minimum (B) a discontinuity (C) a point of inflection (D) a maximum
At $t=0$, the function $f(t)=\frac{\sin t}{t}$ has(A) a minimum(B) a discontinuity (C) a point of inflection(D) a maximum
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3 votes
2 answers
589
Limits
Please give the answer with full solution.
Please give the answer with full solution.
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0 votes
1 answer
590
maxima minima
maxima minima of 2^(sinx)/2^(cosx)
maxima minima of 2^(sinx)/2^(cosx)
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