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

6 votes

1 answer

GO Classes Test Series 2023 | Calculus | Test 1 | Question: 10
Consider the following statements: $f(x)$ is continuous on $[a, b]$ $f(x)$ is differentiable on $(a, b)$ $f(a)=f(b)$ Which of the above statements are required in order to guarantee a $c \in(a, b)$ such that $f^{\prime}(c)(b-a)=f(b)-f(a) ?$ I only I and II only I, II, and III I and III only

Consider the following statements:$f(x)$ is continuous on $[a, b]$$f(x)$ is differentiable on $(a, b)$$f(a)=f(b)$Which of the above statements are required in order to gu...

GO Classes

550 views

GO Classes asked Aug 28, 2022

7 votes

1 answer

GO Classes Test Series 2023 | Calculus | Test 1 | Question: 11
Let $I=(a, b)$ be an open interval and let $f$ be a function which is differentiable on $I$. Which of the followings is/are true statements - If $f^{\prime}(x)=0$ for all $x \in I$, then there is a constant $r$ such that $f(x)=r$ ... decreasing on $I$. If $f^{\prime}(x)>0$ for all $x \in I$, then $f(x)$ is strictly decreasing on $I$.

Let $I=(a, b)$ be an open interval and let $f$ be a function which is differentiable on $I$. Which of the followings is/are true statements -If $f^{\prime}(x)=0$ for all ...

GO Classes

573 views

GO Classes asked Aug 28, 2022

8 votes

1 answer

GO Classes Test Series 2023 | Calculus | Test 1 | Question: 12
Which of the following is/are FALSE? The absolute maximum value of $f(x)=\dfrac{1}{x}$ on the interval $[2,4]$ is $2.$ If $f(x)$ is a continuous function and $f(3)=2$ and $f(5)=-1$, then $f(x)$ has a root between $3$ and $5 .$ ... $h(x)$ is a continuous function and $h(1)=4$ and $h(2)=5$, then $h(x)$ has no roots between $1$ and $2.$

Which of the following is/are FALSE?The absolute maximum value of $f(x)=\dfrac{1}{x}$ on the interval $[2,4]$ is $2.$If $f(x)$ is a continuous function and $f(3)=2$ and $...

GO Classes

593 views

GO Classes asked Aug 28, 2022

6 votes

1 answer

GO Classes Test Series 2023 | Calculus | Test 1 | Question: 13
Suppose $g(x)$ is a polynomial function such that $g(-1)=4$ and $g(2)=7$. Then there is a number $c$ between $-1$ and $2$ such that $g(c)=1$ $g^{\prime}(c)=1$ $g(c)=0$ $g^{\prime}(c)=0$

Suppose $g(x)$ is a polynomial function such that $g(-1)=4$ and $g(2)=7$. Then there is a number $c$ between $-1$ and $2$ such that$g(c)=1$$g^{\prime}(c)=1$$g(c)=0$$g^{\p...

GO Classes

666 views

GO Classes asked Aug 28, 2022

2 votes

2 answers

GO Classes Test Series 2023 | Calculus | Test | Question: 14
Which of the following limit is/are correct? $\displaystyle{}\lim _{x \rightarrow \infty} \sqrt[x]{x}=1$ $\displaystyle{}\lim _{x \rightarrow \infty} \sqrt[x]{x}=e$ $\displaystyle{}\lim _{x \rightarrow \infty}\left(1+\frac{2}{x}\right)^{x}=e^{2}$ $\displaystyle{}\lim _{x \rightarrow \infty}\left(1+\frac{2}{x}\right)^{x}=e$

Which of the following limit is/are correct?$\displaystyle{}\lim _{x \rightarrow \infty} \sqrt[x]{x}=1$$\displaystyle{}\lim _{x \rightarrow \infty} \sqrt[x]{x}=e$$\displa...

GO Classes

487 views

GO Classes asked Aug 28, 2022

6 votes

1 answer

GO Classes Test Series 2023 | Calculus | Test 1 | Question: 15
Suppose $f$ is twice differentiable with $ f^{\prime \prime}(x)=7 x-2, \quad f^{\prime}(-2)=0, \quad \text { and } \quad f(-2)=-2 . $ Find $f(0)$. $-337 / 6$ $-74 / 3$ $23 / 9$ $37 / 4$

Suppose $f$ is twice differentiable with$$f^{\prime \prime}(x)=7 x-2, \quad f^{\prime}(-2)=0, \quad \text { and } \quad f(-2)=-2 .$$Find $f(0)$.$-337 / 6$$-74 / 3$$23 / 9...

GO Classes

562 views

GO Classes asked Aug 28, 2022

4 votes

1 answer

GO Classes Test Series 2023 | Calculus | Test 1 | Question: 16
The sum of three positive numbers is $12$ and two of them are equal. Find the largest possible product. $86$ $64$ $48$ $72$

The sum of three positive numbers is $12$ and two of them are equal. Find the largest possible product.$86$$64$$48$$72$

GO Classes

503 views

GO Classes asked Aug 28, 2022

3 votes

2 answers

GO Classes Test Series 2023 | Calculus | Test 1 | Question: 17
If $f(x)=e^{x} g(x), g(0)=2$ and $g^{\prime}(0)=1$, then $f^{\prime}(0)$ is $1$ $3$ $2$ $0$

If $f(x)=e^{x} g(x), g(0)=2$ and $g^{\prime}(0)=1$, then $f^{\prime}(0)$ is$1$$3$$2$$0$

GO Classes

385 views

GO Classes asked Aug 28, 2022

6 votes

1 answer

GO Classes Test Series 2023 | Calculus | Test 1 | Question: 18
Let $f$ be differentiable for all $x$. If $f(1)=-2$ and $f^{\prime}(x) \geq 2$ for $x \in[1,6]$, then $f(6) \geq 8$ $f(6)<8$ $f(6)<5$ $f(6)=5$

Let $f$ be differentiable for all $x$. If $f(1)=-2$ and $f^{\prime}(x) \geq 2$ for $x \in[1,6]$, then$f(6) \geq 8$$f(6)<8$$f(6)<5$$f(6)=5$

GO Classes

458 views

GO Classes asked Aug 28, 2022

8 votes

1 answer

GO Classes Test Series 2023 | Calculus | Test 1 | Question: 19
The equation $x^{5}+x+1=0$ has a solution in the interval $[0,1]$ $[-1,0]$ $[-2,-1]$ $[1,2]$

The equation $x^{5}+x+1=0$ has a solution in the interval$[0,1]$$[-1,0]$$[-2,-1]$$[1,2]$

GO Classes

525 views

GO Classes asked Aug 28, 2022

2 votes

1 answer

GO Classes Test Series 2023 | Calculus | Test 1 | Question: 20
Which of the following expression evaluates to given integral $ \int \frac{\ln (\ln x)}{x \ln x} d x $ $\dfrac{\ln x}{x}+C$ $\frac{1}{2}(\ln \ln x)^{2}+C$ $(\ln x)^{2}+C$ $(\ln \ln x)+C$

Which of the following expression evaluates to given integral$$\int \frac{\ln (\ln x)}{x \ln x} d x$$$\dfrac{\ln x}{x}+C$$\frac{1}{2}(\ln \ln x)^{2}+C$$(\ln x)^{2}+C$$(\l...

GO Classes

539 views

GO Classes asked Aug 28, 2022

1 votes

0 answers

Engineering Mathematics
Please verify the solution(the differentiation part ),

Please verify the solution(the differentiation part ),

Overflow04

597 views

Overflow04 asked Aug 21, 2022

0 votes

1 answer

Maths for natural science
Determine the domain of the function $f(x)=\left | x \right |+1$

Determine the domain of the function $f(x)=\left | x \right |+1$

Hailemariam

311 views

Hailemariam asked Aug 5, 2022

0 votes

1 answer

Mathematics for Natural Science
Determine the domain of the function $f(x) = |x – 2|$

Determine the domain of the function $f(x) = |x – 2|$

Hailemariam

246 views

Hailemariam asked Aug 3, 2022

0 votes

0 answers

Mathematics for Natural Science
Sketch the graph of $f(x) = \frac{x^{3}-1}{x^{2}-1}$

Sketch the graph of $f(x) = \frac{x^{3}-1}{x^{2}-1}$

kidussss

377 views

kidussss asked Jul 29, 2022

1 votes

2 answers

Applied Mathematics Calculus and Limit Question
Evaluate the question of the following limits. $\lim_{x\rightarrow 1} \frac{x}{(x-1)^{2}}$

Evaluate the question of the following limits. $\lim_{x\rightarrow 1} \frac{x}{(x-1)^{2}}$

kidussss

864 views

kidussss asked Jul 8, 2022

0 votes

1 answer

Applied Mathematics Derivative
Please find derivation of the following equation. Let $f(x)=e^{x^{2}}\ln x,$ then find, ${f}'(x)$.

Please find derivation of the following equation.Let $f(x)=e^{x^{2}}\ln x,$ then find, ${f}'(x)$.

kidussss

319 views

kidussss asked Jul 8, 2022

0 votes

2 answers

Applied Mathematics Calculus and Limit Question
Evaluate the question of the following limits. $\lim_{x\rightarrow \infty} \frac{2x^{3}+3x-5}{5x^{3}+1}$

Evaluate the question of the following limits. $\lim_{x\rightarrow \infty} \frac{2x^{3}+3x-5}{5x^{3}+1}$

kidussss

463 views

kidussss asked Jul 8, 2022

0 votes

3 answers

Applied Mathematics Question
Let $f(x) = e^{x^2},$ then find $f''(x).$

Let $f(x) = e^{x^2},$ then find $f''(x).$

kidussss

451 views

kidussss asked Jul 7, 2022

0 votes

0 answers

iit kanpur Calculas practice question
Does there exist a differentiable function f : [0, 2] → R satisfying f(0) = −1, f(2) = 4 and f’(x) ≤ 2 for all x ∈ [0, 2]?

Does there exist a differentiable function f : [0, 2] → R satisfying f(0) = −1, f(2) = 4 and f’(x) ≤ 2 for all x ∈ [0, 2]?

Kabir5454

316 views

Kabir5454 asked May 16, 2022

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