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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

#1
1.1k
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3 answers
2 votes
GATE DS&AI 2024 | Question: 50
Evaluate the following limit:\[\lim _{x \rightarrow 0} \frac{\ln \left(\left(x^{2}+1\right) \cos x\right)}{x^{2}}= \]
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#2
3.1k
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2 answers
5 votes
GATE CSE 2024 | Set 2 | Question: 6
​​​​​Let $f(x)$ be a continuous function from $\mathbb{R}$ to $\mathbb{R}$ such that\[f(x)=1-f(2-x)\]Which one of the following options is the CORRECT value of $\int_{0}^{2} f(x) d x$ ?$0$1$2$-1$
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#3
4.3k
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2 answers
11 votes
GATE CSE 2024 | Set 1 | Question: 1
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function such that $f(x)=\max \left\{x, x^3\right\}, x \in \mathbb{R}$, where $\mathbb{R}$ is the set of all real numbers. ... $\{-2,-1,1\}$\{0,1\}$\{-1,0,1\}$
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#4
696
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2 answers
1 votes
Memory Based GATE DA 2024 | Question: 3
Evaluate the limit:\[\lim_{{x \to 0}} \frac{\ln \left(\left(x^2+1\right) \cos x\right)}{x^2}\]
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#5
448
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1 answers
0 votes
Memory Based GATE DA 2024 | Question: 7
Consider the function \(f(x) = \frac{1}{1+e^{-x}}\). Determine the derivative \(f^{\prime}(x)\) when \(f(x) = 0.4\).
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#6
263
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0 answers
1 votes
Memory Based GATE DA 2024 | Question: 28
Consider a function \(f\) with \(f^1(X^*) = 0\) and \(f^{1l}(X^*) > 0\). Based on these conditions, determine the nature of the critical point \(X^*\) for ... X^*\) is a local minimum\(X^*\) is a global maximum\(X^*\) is a global minimum
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#7
334
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1 answers
2 votes
Memory Based GATE DA 2024 | Question: 30
Consider the function \( F(x) \) defined as follows:\[ F(x) = \left\{\begin{array}{cc}    -x & \text{if } x < -2 \\    ax^2 + bx + c & \text{if ... ) and \( c \) such that \( F(x) \) is continuous and differentiable over its entire domain.
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#8
252
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0 answers
0 votes
Memory Based GATE DA 2024 | Question: 52
Consider the function \(f(x) = \frac{x^4}{4} - \frac{2x^3}{3} - \frac{3x^2}{2}\).Which of the following statements about the critical points of \(f(x)\) are correct? ... maxima at \(x = 0\)Local minima at \(x = 3\)Local minima at \(x = -1\)
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#9
996
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2 answers
7 votes
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 11
Let $f(x)$ be a real-valued function all of whose derivatives exist. Recall that a point $x_0$ in the domain is called an inflection point of $f(x)$ ... and $x_0=6$, both are inflection points.The function does not have an inflection point.
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#10
800
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2 answers
4 votes
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 37
Which of the following is/are TRUE?There is a differentiable function $f(x)$ with the property that $f(1)=-2$ and $f(5)=14$ and $f^{\prime}(x)\lt 3$ for ... $f$ is differentiable at the number $x$, then it is continuous at $x$.
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#11
620
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1 answers
4 votes
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 31
If $f, f^{\prime}$, and $f^{\prime \prime}$ are continuous and $f(2)=0, f^{\prime}(2)=2$, and $f^{\prime \prime}(2)=-3$, what can we say about the function ... $.$f$ is increasing, at $x=2$f$ is decreasing, at $x=2$
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#12
160
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0 answers
0 votes
GATE 2019 | MATHS | LIMIT
Let $ u_n = \frac{(n!)!}{1 \cdot 3 \cdot 5 \cdots (2n - 1)} $ (the set of all natural numbers).Then $ \lim\limits_{n \to \infty} \frac{n}{u_n} $ is equal to ______________
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#13
127
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0 answers
0 votes
GATE 2022 | MATHS | Q-32
If the function \( f(x, y) = x^2 + xy + y^2 + \frac{1}{x} + \frac{1}{y} \), \( x \neq 0, y \neq 0 \), attains its local minimum value at the point \((a, b)\), then the value of \(a^3 + b^3\) is _________(rounded off to TWO decimal places).
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#14
206
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1 answers
0 votes
Rolle's Mean Value Theorem
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#15
372
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2 answers
2 votes
Evaluate the limit without using L' Hospital Rule.
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#16
183
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1 answers
0 votes
Limit
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#17
864
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1 answers
1 votes
GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 5
$\lim _{x \rightarrow 2} \frac{\sqrt{x}-\sqrt{2}}{x-2}$0$\sqrt{2}$\frac{1}{2 \sqrt{2}}$\frac{1}{\sqrt{2}}$
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#18
399
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0 answers
0 votes
Made Easy Test Series 2024
please anyone explain this question .?
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#19
159
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1 answers
7 votes
GO Classes 2025 | Weekly Quiz 21 | Calculus | Question: 1
Let $f$ ... $\displaystyle{}\int_3^6 f\left(\frac{1}{3} t\right) d t$
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#20
105
views
2 answers
4 votes
GO Classes 2025 | Weekly Quiz 21 | Calculus | Question: 2
Which of the following represents the value of $\displaystyle{}\int_1^e \frac{\ln (x)}{x} d x ?$1$2$1 / 2$e$
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