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Webpage for Calculus:
Recent questions tagged calculus
5
votes
2
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1
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
2.6k
views
Arjun
asked
Feb 16
Calculus
gatecse2024-set2
calculus
definite-integral
+
–
2
votes
2
answers
2
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
3.8k
views
Arjun
asked
Feb 16
Calculus
gatecse2024-set1
calculus
differentiation
+
–
1
votes
2
answers
3
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
610
views
GO Classes
asked
Feb 4
Calculus
gate2024-da-memory-based
goclasses
calculus
limits
numerical-answers
+
–
0
votes
1
answer
4
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
382
views
GO Classes
asked
Feb 4
Calculus
gate2024-da-memory-based
goclasses
calculus
maxima-minima
numerical-answers
+
–
1
votes
0
answers
5
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
219
views
GO Classes
asked
Feb 4
Calculus
gate2024-da-memory-based
goclasses
calculus
maxima-minima
+
–
1
votes
1
answer
6
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
278
views
GO Classes
asked
Feb 4
Calculus
gate2024-da-memory-based
goclasses
calculus
continuity
+
–
0
votes
0
answers
7
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
208
views
GO Classes
asked
Feb 4
Calculus
gate2024-da-memory-based
goclasses
calculus
maxima-minima
+
–
7
votes
2
answers
8
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
933
views
GO Classes
asked
Jan 28
Calculus
goclasses2024-mockgate-13
goclasses
calculus
maxima-minima
1-mark
+
–
3
votes
2
answers
9
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
744
views
GO Classes
asked
Jan 21
Calculus
goclasses2024-mockgate-12
goclasses
calculus
differentiation
multiple-selects
2-marks
+
–
3
votes
1
answer
10
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
564
views
GO Classes
asked
Jan 13
Calculus
goclasses2024-mockgate-11
goclasses
calculus
maxima-minima
1-mark
+
–
0
votes
0
answers
11
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
138
views
rajveer43
asked
Jan 10
Calculus
calculus
+
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