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Search results for calculus
74
votes
11
answers
1
GATE CSE 2014 Set 1 | Question: 47
A function $f(x)$ is continuous in the interval $[0,2]$. It is known that $f(0) = f(2) = -1$ and $f(1) = 1$. Which one of the following statements must be true? There exists a $y$ in the interval $(0,1)$ such that $f(y) = f(y+1)$ For every $y$ ... the function in the interval $(0,2)$ is $1$ There exists a $y$ in the interval $(0,1)$ such that $f(y)$ = $-f(2-y)$
A function $f(x)$ is continuous in the interval $[0,2]$. It is known that $f(0) = f(2) = -1$ and $f(1) = 1$. Which one of the following statements must be true?There exis...
go_editor
20.7k
views
go_editor
asked
Sep 28, 2014
Calculus
gatecse-2014-set1
calculus
continuity
normal
+
–
54
votes
5
answers
2
GATE CSE 2017 Set 1 | Question: 41
Consider a database that has the relation schemas EMP(EmpId, EmpName, DeptId), and DEPT(DeptName, DeptId). Note that the DeptId can be permitted to be NULL in the relation EMP. Consider the following queries on the database expressed in tuple relational calculus. { ... Which of the above queries are safe? I and II only I and III only II and III only I, II and III
Consider a database that has the relation schemas EMP(EmpId, EmpName, DeptId), and DEPT(DeptName, DeptId). Note that the DeptId can be permitted to be NULL in the relatio...
Arjun
25.2k
views
Arjun
asked
Feb 14, 2017
Databases
gatecse-2017-set1
databases
relational-calculus
safe-query
normal
+
–
43
votes
5
answers
3
GATE IT 2007 | Question: 65
Consider a selection of the form $\sigma_{A\leq 100} (r)$, where $r$ is a relation with $1000$ tuples. Assume that the attribute values for $A$ among the tuples are uniformly distributed in the interval $[0, 500].$ Which one of the following options is the best estimate of the number of tuples returned by the given selection query ? $50$ $100$ $150$ $200$
Consider a selection of the form $\sigma_{A\leq 100} (r)$, where $r$ is a relation with $1000$ tuples. Assume that the attribute values for $A$ among the tuples are unifo...
Ishrat Jahan
12.5k
views
Ishrat Jahan
asked
Oct 30, 2014
Databases
gateit-2007
databases
relational-calculus
probability
normal
+
–
16
votes
3
answers
4
GATE CSE 2021 Set 2 | Question: 25
Suppose that $f: \mathbb{R} \rightarrow \mathbb{R}$ is a continuous function on the interval $[-3, 3]$ and a differentiable function in the interval $(-3,3)$ such that for every $x$ in the interval, $f’(x) \leq 2$. If $f(-3)=7$, then $f(3)$ is at most __________
Suppose that $f: \mathbb{R} \rightarrow \mathbb{R}$ is a continuous function on the interval $[-3, 3]$ and a differentiable function in the interval $(-3,3)$ such that fo...
Arjun
6.1k
views
Arjun
asked
Feb 18, 2021
Calculus
gatecse-2021-set2
numerical-answers
calculus
continuity
1-mark
+
–
2
votes
2
answers
5
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
3.3k
views
Arjun
asked
Feb 16
Calculus
gatecse2024-set1
calculus
+
–
95
votes
6
answers
6
GATE CSE 2007 | Question: 60
Consider the relation employee(name, sex, supervisorName) with name as the key, supervisorName gives the name of the supervisor of the employee under consideration. What does the following Tuple Relational Calculus query produce? ... immediate male subordinates. Names of employees with no immediate female subordinates. Names of employees with a female supervisor.
Consider the relation employee(name, sex, supervisorName) with name as the key, supervisorName gives the name of the supervisor of the employee under consideration. What ...
Kathleen
23.3k
views
Kathleen
asked
Sep 21, 2014
Databases
gatecse-2007
databases
relational-calculus
normal
+
–
14
votes
7
answers
7
GATE CSE 2019 | Question: 13
Compute $\displaystyle \lim_{x \rightarrow 3} \frac{x^4-81}{2x^2-5x-3}$ $1$ $53/12$ $108/7$ Limit does not exist
Compute $\displaystyle \lim_{x \rightarrow 3} \frac{x^4-81}{2x^2-5x-3}$$1$$53/12$$108/7$Limit does not exist
Arjun
6.3k
views
Arjun
asked
Feb 7, 2019
Calculus
gatecse-2019
engineering-mathematics
calculus
limits
1-mark
+
–
5
votes
2
answers
8
GATE CSE 2023 | Question: 21
The value of the definite integral \[ \int_{-3}^{3} \int_{-2}^{2} \int_{-1}^{1}\left(4 x^{2} y-z^{3}\right) \mathrm{d} z \mathrm{~d} y \mathrm{~d} x \] is _________. (Rounded off to the nearest integer)
The value of the definite integral \[\int_{-3}^{3} \int_{-2}^{2} \int_{-1}^{1}\left(4 x^{2} y-z^{3}\right) \mathrm{d} z \mathrm{~d} y \mathrm{~d} x\]is _________. (Rounde...
admin
8.5k
views
admin
asked
Feb 15, 2023
Calculus
gatecse-2023
calculus
definite-integral
numerical-answers
1-mark
+
–
8
votes
2
answers
9
GATE CSE 2023 | Question: 18
Let $\qquad f(x)=x^{3}+15 x^{2}-33 x-36$ be a real-valued function. Which of the following statements is/are $\text{TRUE}?$ $f(x)$ does not have a local maximum. $f(x)$ has a local maximum. $f(x)$ does not have a local minimum. $f(x)$ has a local minimum.
Let $$\qquad f(x)=x^{3}+15 x^{2}-33 x-36$$be a real-valued function.Which of the following statements is/are $\text{TRUE}?$$f(x)$ does not have a local maximum.$f(x)$ has...
admin
5.1k
views
admin
asked
Feb 15, 2023
Calculus
gatecse-2023
calculus
maxima-minima
multiple-selects
1-mark
+
–
4
votes
1
answer
10
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
2.0k
views
Arjun
asked
Feb 16
Calculus
gatecse2024-set2
calculus
definite-integral
+
–
36
votes
2
answers
11
GATE CSE 2008 | Question: 25
A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve $3x^4-16x^3+24x^2+37$ is $0$ $1$ $2$ $3$
A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve $3x^4-16x^3+24x^2+37$ is$0$$1$$2$$3...
Kathleen
8.4k
views
Kathleen
asked
Sep 11, 2014
Calculus
gatecse-2008
calculus
maxima-minima
easy
+
–
7
votes
2
answers
12
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
797
views
GO Classes
asked
Jan 28
Calculus
goclasses2024-mockgate-13
goclasses
calculus
maxima-minima
1-mark
+
–
46
votes
6
answers
13
GATE CSE 2001 | Question: 2.24
Which of the following relational calculus expression is not safe? $\left\{t \mid \exists u \in R_1\left(t[A] = u[A]\right) \land \neg \exists s \in R_2 \left(t[A] = s[A]\right)\right\}$ ...
Which of the following relational calculus expression is not safe?$\left\{t \mid \exists u \in R_1\left(t[A] = u[A]\right) \land \neg \exists s \in R_2 \left(t[A] = s[A]\...
Kathleen
8.5k
views
Kathleen
asked
Sep 14, 2014
Databases
gatecse-2001
relational-calculus
normal
databases
+
–
1
votes
2
answers
14
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
444
views
GO Classes
asked
Feb 4
Calculus
gate2024-da-memory-based
goclasses
calculus
limits
numerical-answers
+
–
26
votes
6
answers
15
GATE CSE 2015 Set 1 | Question: 4
$\displaystyle \lim_{x\rightarrow \infty } x^{ \tfrac{1}{x}}$ is $\infty $ $0$ $1$ Not defined
$\displaystyle \lim_{x\rightarrow \infty } x^{ \tfrac{1}{x}}$ is$\infty $$0$$1$Not defined
makhdoom ghaya
8.2k
views
makhdoom ghaya
asked
Feb 11, 2015
Calculus
gatecse-2015-set1
calculus
limits
normal
+
–
1
votes
2
answers
16
Evaluate the limit without using L' Hospital Rule.
Debargha Mitra Roy
253
views
Debargha Mitra Roy
asked
Nov 26, 2023
Calculus
limits
calculus
+
–
25
votes
9
answers
17
GATE CSE 2008 | Question: 1
$\displaystyle \lim_{x \to \infty}\frac{x-\sin x}{x+\cos x}$ equals $1$ $-1$ $\infty$ $-\infty$
$\displaystyle \lim_{x \to \infty}\frac{x-\sin x}{x+\cos x}$ equals$1$$-1$$\infty$$-\infty$
Kathleen
10.0k
views
Kathleen
asked
Sep 11, 2014
Calculus
gatecse-2008
calculus
limits
easy
+
–
3
votes
1
answer
18
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
468
views
GO Classes
asked
Jan 13
Calculus
goclasses2024-mockgate-11
goclasses
calculus
maxima-minima
1-mark
+
–
3
votes
2
answers
19
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
610
views
GO Classes
asked
Jan 21
Calculus
goclasses2024-mockgate-12
goclasses
calculus
differentiation
multiple-selects
2-marks
+
–
0
votes
1
answer
20
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
281
views
GO Classes
asked
Feb 4
Calculus
gate2024-da-memory-based
goclasses
calculus
maxima-minima
numerical-answers
+
–
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