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

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

Recent questions in Calculus

1 votes

1 answer

GATE DS&AI 2024 | Question: 50
Evaluate the following limit: \[ \lim _{x \rightarrow 0} \frac{\ln \left(\left(x^{2}+1\right) \cos x\right)}{x^{2}}= \]

Evaluate the following limit:\[\lim _{x \rightarrow 0} \frac{\ln \left(\left(x^{2}+1\right) \cos x\right)}{x^{2}}= \]

Arjun

826 views

Arjun asked Feb 16

5 votes

1 answer

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 $\int_{0}^{2} f(x) d x$ ? $0$ $1$ $2$ $-1$

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 ...

Arjun

2.2k views

Arjun asked Feb 16

2 votes

2 answers

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. The set of all points where $f(x)$ is NOT differentiable is $\{-1,1,2\}$ $\{-2,-1,1\}$ $\{0,1\}$ $\{-1,0,1\}$

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....

Arjun

3.5k views

Arjun asked Feb 16

1 votes

2 answers

Memory Based GATE DA 2024 | Question: 3
Evaluate the limit: \[ \lim_{{x \to 0}} \frac{\ln \left(\left(x^2+1\right) \cos x\right)}{x^2} \]

Evaluate the limit:\[\lim_{{x \to 0}} \frac{\ln \left(\left(x^2+1\right) \cos x\right)}{x^2}\]

GO Classes

502 views

GO Classes asked Feb 4

0 votes

1 answer

Memory Based GATE DA 2024 | Question: 7
Consider the function $f(x) = \frac{1}{1+e^{-x}}$. Determine the derivative $f^{\prime}(x)$ when $f(x) = 0.4$.

Consider the function $f(x) = \frac{1}{1+e^{-x}}$. Determine the derivative $f^{\prime}(x)$ when $f(x) = 0.4$.

GO Classes

323 views

GO Classes asked Feb 4

1 votes

0 answers

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 the function $f(X)$. $X^*$ is a local maximum $X^*$ is a local minimum $X^*$ is a global maximum $X^*$ is a global minimum

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 the function \(f...

GO Classes

175 views

GO Classes asked Feb 4

1 votes

1 answer

Memory Based GATE DA 2024 | Question: 30
Consider the function $ F(x) $ defined as follows: \[ F(x) = \left\{ \begin{array}{cc} -x & \text{if } x < -2 \\ ax^2 + bx + c & \text{if } x \in [-2, 2] \\ x & \text{if } x > 2 \end{ ... \] \noindent Determine the values of $ a, b, $ and $ c $ such that $ F(x) $ is continuous and differentiable over its entire domain.

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 } x \in [-2, 2] \\...

GO Classes

233 views

GO Classes asked Feb 4

0 votes

0 answers

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? Local minima at $x = 0$ Local maxima at $x = 0$ Local minima at $x = 3$ Local minima at $x = -1$

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?Local...

GO Classes

166 views

GO Classes asked Feb 4

7 votes

2 answers

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 $f(x)$ if the second derivative $f^{\prime \prime}(x)$ changes sign at ... only inflection point. $x_0=0$ and $x_0=6$, both are inflection points. The function does not have an inflection point.

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 $f(x)$ if the second derivat...

GO Classes

855 views

GO Classes asked Jan 28

3 votes

2 answers

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 every real number $x$. There exists a function $f$ ... $a\lt c\lt b$ and $f(c)=0$. If $f$ is differentiable at the number $x$, then it is continuous at $x$.

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 every real number...

GO Classes

657 views

GO Classes asked Jan 21

3 votes

1 answer

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 $f(x)$ at $x=2?$ $f$ has a local minimum at $x=2$. $f$ has a local maximum at $x=2$. $f$ is increasing, at $x=2$ $f$ is decreasing, at $x=2$

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 $f(x)$ at $x=2...

GO Classes

508 views

GO Classes asked Jan 13

0 votes

0 answers

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 ______________

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 _____________...

rajveer43

118 views

rajveer43 asked Jan 10

0 votes

0 answers

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).

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 va...

rajveer43

84 views

rajveer43 asked Jan 10

0 votes

1 answer

Rolle's Mean Value Theorem

Debargha Mitra Roy

181 views

Debargha Mitra Roy asked Dec 1, 2023

1 votes

2 answers

Evaluate the limit without using L' Hospital Rule.

Debargha Mitra Roy

282 views

Debargha Mitra Roy asked Nov 26, 2023

0 votes

1 answer

Limit

Debargha Mitra Roy

143 views

Debargha Mitra Roy asked Nov 26, 2023

1 votes

1 answer

GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 5
$\lim _{x \rightarrow 2} \frac{\sqrt{x}-\sqrt{2}}{x-2}$ $0$ $\sqrt{2}$ $\frac{1}{2 \sqrt{2}}$ $\frac{1}{\sqrt{2}}$

$\lim _{x \rightarrow 2} \frac{\sqrt{x}-\sqrt{2}}{x-2}$$0$$\sqrt{2}$$\frac{1}{2 \sqrt{2}}$$\frac{1}{\sqrt{2}}$

admin

798 views

admin asked Oct 21, 2023

0 votes

0 answers

Made Easy Test Series 2024
please anyone explain this question .?

please anyone explain this question .?

Ray Tomlinson

364 views

Ray Tomlinson asked Oct 12, 2023

3 votes

2 answers

TIFR CSE 2023 | Part A | Question: 6
For a function $f: \mathbb{R} \rightarrow \mathbb{R},$ consider the following conditions. $\text{(C1)}$ $|f(x)| \leq|x|$ for all $x \in \mathbb{R}$. $\text{(C2)}$ $|f(x)| \leq|x|^{2}$ for all $x \in \mathbb{R}$. $\text{(C3)}$ ... $\text{(C3)}$ only Conditions $\text{(C1)}$ and $\text{(C2)}$ only Conditions $\text{(C2)}$ and $\text{(C3)}$ only

For a function $f: \mathbb{R} \rightarrow \mathbb{R},$ consider the following conditions.$\text{(C1)}$ $|f(x)| \leq|x|$ for all $x \in \mathbb{R}$.$\text{(C2)}$ $|f(x)| \...

admin

466 views

admin asked Mar 14, 2023

2 votes

1 answer

TIFR CSE 2023 | Part A | Question: 7
Suppose $f(x)$ is a polynomial of the form $a x^{2}+b x+c,$ with $a, b, c$ unknown real numbers. Suppose you are additionally told that $f(1)=2$ and $f(-1)=3$. Consider the following four statements. $\text{(S1)}$ $f(0)$ cannot be ... $\text{(S4)}$ only Statement $\text{(S3)}$ only Statements $\text{(S3)}$ and $\text{(S4)}$ only All four statements are true

Suppose $f(x)$ is a polynomial of the form $a x^{2}+b x+c,$ with $a, b, c$ unknown real numbers. Suppose you are additionally told that $f(1)=2$ and $f(-1)=3$. Consider t...

admin

453 views

admin asked Mar 14, 2023

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