Login
Register
Dark Mode
Brightness
Profile
Edit Profile
Messages
My favorites
My Updates
Logout
Webpage for Calculus:
Recent questions tagged calculus
15
votes
5
answers
511
TIFR CSE 2015 | Part A | Question: 11
Suppose that $f(x)$ is a continuous function such that $0.4 \leq f(x) \leq 0.6$ for $0 \leq x \leq 1$. Which of the following is always true? $f(0.5) = 0.5$. There exists $x$ between $0$ and $1$ such that $f(x) = 0.8x$. There exists $x$ between $0$ and $0.5$ such that $f(x) = x$. $f(0.5) > 0.5$. None of the above statements are always true.
Suppose that $f(x)$ is a continuous function such that $0.4 \leq f(x) \leq 0.6$ for $0 \leq x \leq 1$. Which of the following is always true?$f(0.5) = 0.5$.There exists $...
makhdoom ghaya
2.8k
views
makhdoom ghaya
asked
Dec 5, 2015
Calculus
tifr2015
maxima-minima
calculus
+
–
5
votes
0
answers
512
TIFR CSE 2015 | Part A | Question: 10
Let $f(x), x\in \left[0, 1\right]$, be any positive real valued continuous function. Then $\displaystyle \lim_{n \rightarrow \infty} (n + 1) \int_{0}^{1} x^{n} f(x) \text{d}x$ equals. $\max_{x \in \left[0, 1\right]} f(x)$ $\min_{x \in \left[0, 1\right]} f(x)$ $f(0)$ $f(1)$ $\infty$
Let $f(x), x\in \left[0, 1\right]$, be any positive real valued continuous function. Then $\displaystyle \lim_{n \rightarrow \infty} (n + 1) \int_{0}^{1} x^{n} f(...
makhdoom ghaya
707
views
makhdoom ghaya
asked
Dec 5, 2015
Calculus
tifr2015
calculus
limits
definite-integral
+
–
1
votes
2
answers
513
Find absolute minimum
Himanshu1
725
views
Himanshu1
asked
Dec 4, 2015
Calculus
maxima-minima
calculus
+
–
4
votes
2
answers
514
What is the maximum value of $\dfrac{e^{\sin x}}{e^{\cos x}}$ where $x$ is a real number?
radha gogia
6.1k
views
radha gogia
asked
Nov 22, 2015
Calculus
calculus
maxima-minima
+
–
2
votes
1
answer
515
Algorithm
A polynomial p(x) is such that p(0)=5 ,p(1)=4 ,p(2)=9 and p(3)=20 The minimum degree it can have is..
A polynomial p(x) is such that p(0)=5 ,p(1)=4 ,p(2)=9 and p(3)=20 The minimum degree it can have is..
Soumyashree
485
views
Soumyashree
asked
Nov 21, 2015
Calculus
calculus
polynomials
numerical-answers
+
–
1
votes
2
answers
516
How to solve below equation ?
The value of $\frac{(1-i\sqrt 3)^{30}}{ (1+i)^{60}} \left( i = \sqrt {-1}\right)$ is ______. 1 0 -1 2
The value of $\frac{(1-i\sqrt 3)^{30}}{ (1+i)^{60}} \left( i = \sqrt {-1}\right)$ is ______.10-12
radha gogia
567
views
radha gogia
asked
Nov 18, 2015
Calculus
calculus
complex-number
+
–
9
votes
6
answers
517
TIFR CSE 2014 | Part A | Question: 9
Solve min $x^{2}+y^{2}$ subject to $\begin {align*} x + y &\geq 10,\\ 2x + 3y &\geq 20,\\ x &\geq 4,\\ y &\geq 4. \end{align*}$ $32$ $50$ $52$ $100$ None of the above
Solve min $x^{2}+y^{2}$ subject to$$\begin {align*} x + y &\geq 10,\\2x + 3y &\geq 20,\\x &\geq 4,\\y &\geq 4.\end{align*}$$$32$$50$$52$$100$None of the above
makhdoom ghaya
1.8k
views
makhdoom ghaya
asked
Nov 9, 2015
Calculus
tifr2014
calculus
maxima-minima
+
–
8
votes
2
answers
518
TIFR CSE 2013 | Part A | Question: 16
The minimum of the function $f(x) = x \log_{e}(x)$ over the interval $[\frac{1}{2}, \infty )$ is $0$ $-e$ $\frac{-\log_{e}(2)}{2}$ $\frac{-1}{e}$ None of the above
The minimum of the function $f(x) = x \log_{e}(x)$ over the interval $[\frac{1}{2}, \infty )$ is$0$$-e$$\frac{-\log_{e}(2)}{2}$$\frac{-1}{e}$None of the above
makhdoom ghaya
1.4k
views
makhdoom ghaya
asked
Nov 5, 2015
Calculus
tifr2013
calculus
maxima-minima
+
–
1
votes
1
answer
519
integration 10[IN]
http://gateforum.com/wp-content/uploads/2013/01/IN-2010.pdf Question 21 The integral $\int _{-\infty} ^{\infty}\delta (t-\frac{\pi}{6})6\sin(t)dt$ evaluates to (A).6 (B).3 (c).1.5 (D).0
http://gateforum.com/wp-content/uploads/2013/01/IN-2010.pdf Question 21The integral $\int _{-\infty} ^{\infty}\delta (t-\frac{\pi}{6})6\sin(t)dt$ evaluates to(A).6(B).3(c...
monali
1.3k
views
monali
asked
Nov 4, 2015
Calculus
calculus
+
–
8
votes
2
answers
520
TIFR CSE 2012 | Part A | Question: 15
Consider the differential equation $dx/dt= \left(1 - x\right)\left(2 - x\right)\left(3 - x\right)$. Which of its equilibria is unstable? $x=0$ $x=1$ $x=2$ $x=3$ None of the above
Consider the differential equation $dx/dt= \left(1 - x\right)\left(2 - x\right)\left(3 - x\right)$. Which of its equilibria is unstable?$x=0$$x=1$$x=2$$x=3$None of the ab...
makhdoom ghaya
1.9k
views
makhdoom ghaya
asked
Oct 30, 2015
Calculus
tifr2012
calculus
differential-equation
+
–
7
votes
3
answers
521
TIFR CSE 2012 | Part A | Question: 14
The limit $\displaystyle \lim_{n \rightarrow \infty} \left(\sqrt{n^{2}+n}-n\right)$ equals. $\infty$ $1$ $1 / 2$ $0$ None of the above
The limit $\displaystyle \lim_{n \rightarrow \infty} \left(\sqrt{n^{2}+n}-n\right)$ equals.$\infty$$1$$1 / 2$$0$None of the above
makhdoom ghaya
1.8k
views
makhdoom ghaya
asked
Oct 30, 2015
Calculus
tifr2012
calculus
limits
+
–
3
votes
2
answers
522
TIFR CSE 2012 | Part A | Question: 13
The maximum value of the function $f\left(x, y, z\right)= \left(x - 1 / 3\right)^{2}+ \left(y - 1 / 3\right)^{2}+ \left(z - 1 / 3\right)^{2}$ subject to the constraints $x + y + z=1,\quad x \geq 0, y \geq 0, z \geq 0$ is $1 / 3$ $2 / 3$ $1$ $4 / 3$ $4 / 9$
The maximum value of the function$f\left(x, y, z\right)= \left(x - 1 / 3\right)^{2}+ \left(y - 1 / 3\right)^{2}+ \left(z - 1 / 3\right)^{2}$subject to the constraints$x +...
makhdoom ghaya
1.4k
views
makhdoom ghaya
asked
Oct 30, 2015
Calculus
tifr2012
calculus
maxima-minima
+
–
15
votes
2
answers
523
TIFR CSE 2012 | Part A | Question: 12
For the polynomial $p(x)= 8x^{10}-7x^{3}+x-1$ consider the following statements (which may be true or false) It has a root between $[0, 1].$ It has a root between $[0, -1].$ It has no roots outside $(-1, 1).$ Which of the above statements are true? Only (i). Only (i) and (ii). Only (i) and (iii). Only (ii) and (iii). All of (i), (ii) and (iii).
For the polynomial $p(x)= 8x^{10}-7x^{3}+x-1$ consider the following statements (which may be true or false)It has a root between $[0, 1].$It has a root between $[0, -1]....
makhdoom ghaya
1.4k
views
makhdoom ghaya
asked
Oct 30, 2015
Calculus
tifr2012
calculus
polynomials
+
–
12
votes
4
answers
524
TIFR CSE 2011 | Part A | Question: 14
The limit $\lim_{x \to 0} \frac{d}{dx}\,\frac{\sin^2 x}{x}$ is $0$ $2$ $1$ $\frac{1}{2}$ None of the above
The limit $$\lim_{x \to 0} \frac{d}{dx}\,\frac{\sin^2 x}{x}$$ is$0$$2$$1$$\frac{1}{2}$None of the above
makhdoom ghaya
2.3k
views
makhdoom ghaya
asked
Oct 19, 2015
Calculus
tifr2011
calculus
limits
+
–
10
votes
3
answers
525
TIFR CSE 2011 | Part A | Question: 11
$\int_{0}^{1} \log_e(x) dx=$ $1$ $-1$ $\infty $ $-\infty $ None of the above
$$\int_{0}^{1} \log_e(x) dx=$$$1$$-1$$\infty $$-\infty $None of the above
makhdoom ghaya
2.4k
views
makhdoom ghaya
asked
Oct 19, 2015
Calculus
tifr2011
calculus
definite-integral
+
–
10
votes
2
answers
526
TIFR CSE 2011 | Part A | Question: 4
Consider the problem of maximizing $x^{2}-2x+5$ such that $0< x< 2$. The value of $x$ at which the maximum is achieved is: $0.5$ $1$ $1.5$ $1.75$ None of the above
Consider the problem of maximizing $x^{2}-2x+5$ such that $0< x< 2$. The value of $x$ at which the maximum is achieved is:$0.5$$1$$1.5$$1.75$None of the above
makhdoom ghaya
1.7k
views
makhdoom ghaya
asked
Oct 17, 2015
Calculus
tifr2011
calculus
maxima-minima
+
–
2
votes
1
answer
527
TIFR2010-Maths-B-13
Define $\left \{ x_{n} \right \}$ as $x_{1}=0.1,x_{2}=0.101,x_{3}=0.101001,\dots$ Then the sequence $\left \{ x_{n} \right \}$. Converges to a rational number Converges to a irrational number Does not coverage Oscillates
Define $\left \{ x_{n} \right \}$ as $x_{1}=0.1,x_{2}=0.101,x_{3}=0.101001,\dots$ Then the sequence $\left \{ x_{n} \right \}$.Converges to a rational numberConverges to ...
makhdoom ghaya
1.6k
views
makhdoom ghaya
asked
Oct 15, 2015
Calculus
tifrmaths2010
calculus
convergence
+
–
3
votes
2
answers
528
TIFR2010-Maths-B-8
The function $f(x)$ defined by $f(x)= \begin{cases} 0 & \text{if x is rational } \\ x & \text{if } x\text{ is irrational } \end{cases}$ is not continuous at any point is continuous at every point is continuous at every rational number is continuous at $x=0$
The function $f(x)$ defined by $$f(x)= \begin{cases} 0 & \text{if x is rational } \\ x & \text{if } x\text{ is irrational } \end{cases}$$is not continuous at any po...
Arjun
1.1k
views
Arjun
asked
Oct 12, 2015
Calculus
tifrmaths2010
calculus
+
–
3
votes
1
answer
529
TIFR2010-Maths-B-7
Number of solutions of the ordinary differential equation. $\frac{d^{2}y}{dx^{2}}-y=0, y(0)=0, y(\pi )=1$ is 0 is 1 is 2 None of the above
Number of solutions of the ordinary differential equation.$\frac{d^{2}y}{dx^{2}}-y=0, y(0)=0, y(\pi )=1$is 0is 1is 2None of the above
makhdoom ghaya
538
views
makhdoom ghaya
asked
Oct 12, 2015
Calculus
tifrmaths2010
calculus
+
–
2
votes
0
answers
530
TIFR2010-Maths-B-5
If $f_{n}(x)$ are continuous functions from [0, 1] to [0, 1], and $f_{n}(x)\rightarrow f(x)$ as $n\rightarrow \infty $, then which of the following statements is true? $f_{n}(x)$ converges to $f(x)$ uniformly on [0, 1] $f_{n}(x)$ converges to $f(x)$ uniformly on (0, 1) $f(x)$ is continuous on [0, 1] None of the above
If $f_{n}(x)$ are continuous functions from [0, 1] to [0, 1], and $f_{n}(x)\rightarrow f(x)$ as $n\rightarrow \infty $, then which of the following statements is true?$f_...
makhdoom ghaya
556
views
makhdoom ghaya
asked
Oct 11, 2015
Calculus
tifrmaths2010
calculus
convergence
+
–
2
votes
1
answer
531
TIFR2010-Maths-B-1
Let $U_{n}=\sin(\frac{\pi }{n})$ and consider the series $\sum u_{n}$. Which of the following statements is false? $\sum u_{n}$ is convergent $u_{n}\rightarrow 0$ as $n\rightarrow \infty $ $\sum u_{n}$ is divergent $\sum u_{n}$ is absolutely convergent
Let $U_{n}=\sin(\frac{\pi }{n})$ and consider the series $\sum u_{n}$. Which of the following statements is false?$\sum u_{n}$ is convergent$u_{n}\rightarrow 0$ as $n\rig...
makhdoom ghaya
642
views
makhdoom ghaya
asked
Oct 11, 2015
Calculus
tifrmaths2010
calculus
convergence
+
–
2
votes
1
answer
532
TIFR2010-Maths-A-14
The solution of the ordinary differential equation. $\frac{dy}{dx}=y, y(0)=0$ Is unbounded Is positive Is negative Is zero
The solution of the ordinary differential equation.$$\frac{dy}{dx}=y, y(0)=0$$Is unboundedIs positiveIs negativeIs zero
makhdoom ghaya
626
views
makhdoom ghaya
asked
Oct 11, 2015
Calculus
tifrmaths2010
calculus
+
–
4
votes
4
answers
533
TIFR2010-Maths-A-8
Let $f(x)= |x|^{3/2}, x \in \mathbb{R}$. Then $f$ is uniformly continuous. $f$ is continuous, but not differentiable at $x=0$. $f$ is differentiable and $f ' $ is continuous. $f$ is differentiable, but $f ' $ is discontinuous at $x=0$.
Let $f(x)= |x|^{3/2}, x \in \mathbb{R}$. Then$f$ is uniformly continuous.$f$ is continuous, but not differentiable at $x=0$.$f$ is differentiable and $f ' $ is continuous...
makhdoom ghaya
1.4k
views
makhdoom ghaya
asked
Oct 11, 2015
Calculus
tifrmaths2010
calculus
differentiation
continuity
+
–
3
votes
1
answer
534
TIFR2010-Maths-A-6
The maximum value of $f(x)=x^{n}(1 - x)^{n}$ for a natural numbers $n\geq 1$ and $0\leq x\leq 1$ is $\frac{1}{2^{n}}$ $\frac{1}{3^{n}}$ $\frac{1}{5^{n}}$ $\frac{1}{4^{n}}$
The maximum value of $f(x)=x^{n}(1 - x)^{n}$ for a natural numbers $n\geq 1$ and $0\leq x\leq 1$ is$\frac{1}{2^{n}}$$\frac{1}{3^{n}}$$\frac{1}{5^{n}}$$\frac{1}{4^{n}}$
makhdoom ghaya
733
views
makhdoom ghaya
asked
Oct 11, 2015
Calculus
tifrmaths2010
calculus
maxima-minima
+
–
15
votes
6
answers
535
TIFR CSE 2010 | Part A | Question: 7
The limit of $\dfrac{10^{n}}{n!}$ as $n \to \infty$ is. $0$ $1$ $e$ $10$ $\infty$
The limit of $\dfrac{10^{n}}{n!}$ as $n \to \infty$ is.$0$$1$$e$$10$$\infty$
makhdoom ghaya
3.4k
views
makhdoom ghaya
asked
Oct 2, 2015
Calculus
tifr2010
calculus
limits
+
–
7
votes
3
answers
536
TIFR CSE 2010 | Part A | Question: 3
The function $f (x) = 2.5 \log_e \left( 2 + \exp \left( x^2 - 4x + 5 \right)\right)$ attains a minimum at $x = $? $0$ $1$ $2$ $3$ $4$
The function $f (x) = 2.5 \log_e \left( 2 + \exp \left( x^2 - 4x + 5 \right)\right)$ attains a minimum at $x = $?$0$$1$$2$$3$$4$
makhdoom ghaya
2.0k
views
makhdoom ghaya
asked
Oct 2, 2015
Calculus
tifr2010
calculus
maxima-minima
+
–
1
votes
3
answers
537
Calculate the limit
$\lim_{x \to 0} \frac{\cos(x)-\log(1+x)-1+x}{\sin^2x} = ? $ Please explain the steps also
$$\lim_{x \to 0} \frac{\cos(x)-\log(1+x)-1+x}{\sin^2x} = ? $$Please explain the steps also
Salman
922
views
Salman
asked
Aug 1, 2015
Calculus
calculus
limits
+
–
0
votes
3
answers
538
select correct option for limit
$\lim_{x\rightarrow 0}\sin \left( \frac{1}{x}\right)$ (a) 1 (b) 0 (c) does not exist (d) none of these
$\lim_{x\rightarrow 0}\sin \left( \frac{1}{x}\right)$(a) 1(b) 0(c) does not exist(d) none of these
saket nandan
672
views
saket nandan
asked
Jul 10, 2015
Calculus
calculus
limits
+
–
1
votes
1
answer
539
calculate limit
$\lim_{x\rightarrow 0}\frac{ \sin x^{\circ}}{x}$
$\lim_{x\rightarrow 0}\frac{ \sin x^{\circ}}{x}$
saket nandan
415
views
saket nandan
asked
Jul 10, 2015
Calculus
calculus
limits
+
–
0
votes
1
answer
540
calculate limit
$\lim_{x\rightarrow 0} \left( \frac{1}{x^{2}} -\frac{1}{\sin^{2}x} \right)$
$\lim_{x\rightarrow 0} \left( \frac{1}{x^{2}} -\frac{1}{\sin^{2}x} \right)$
saket nandan
386
views
saket nandan
asked
Jul 10, 2015
Calculus
calculus
limits
+
–
Page:
« prev
1
...
13
14
15
16
17
18
19
20
next »
Email or Username
Show
Hide
Password
I forgot my password
Remember
Log in
Register