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Recent questions tagged differentiation
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61
Testbook Test Series: Calculus - Differentiability
If $y = f(x)$ is a solution of $ d^2y/dx^2 = 0$ , with boundary conditions $y=8$ at $x=0$ and $dy/dx =4$ at $x=16$, Find the value of $f(-2)$ When they say, $y = f(x)$ is a solution of $ d^2y/dx^2 = 0$ What does that mean?
If $y = f(x)$ is a solution of $ d^2y/dx^2 = 0$ , with boundary conditions $y=8$ at $x=0$and $dy/dx =4$ at $x=16$, Find the value of $f(-2)$When they say, $y = f(x)$ is ...
shreyansh jain
302
views
shreyansh jain
asked
Dec 18, 2018
Mathematical Logic
testbook-test-series
differentiation
calculus
+
–
1
votes
0
answers
62
NIELIT 2018-19
If $u=f(y-z, \: \: z-x, \: \: x-y)$, then $\frac{ \partial u}{ \partial x} + \frac{ \partial u}{ \partial y} + \frac{ \partial u}{ \partial z} $ is equal to: $x+y+z$ $1+x+y+z$ $1$ $0$
If $u=f(y-z, \: \: z-x, \: \: x-y)$, then $\frac{ \partial u}{ \partial x} + \frac{ \partial u}{ \partial y} + \frac{ \partial u}{ \partial z} $ is equal to:$x+y+z$$1+x+...
Arjun
648
views
Arjun
asked
Dec 7, 2018
Others
nielit-2018
non-gate
differentiation
partial-order
+
–
1
votes
0
answers
63
NIELIT 2018-23
If $w=f(z)=u(x,y)+i \: v(x,y)$ is an analytic function, then $\frac{dw}{dz}$ is: $\frac{ \partial u } {\partial x}- i \frac{ \partial u}{\partial y}$ $\frac{ \partial u } {\partial x}+ i \frac{ \partial v}{\partial y}$ $\frac{ \partial u } {\partial x}- i \frac{ \partial v}{\partial x}$ $\frac{ \partial u } {\partial x}+ i \frac{ \partial u}{\partial y}$
If $w=f(z)=u(x,y)+i \: v(x,y)$ is an analytic function, then $\frac{dw}{dz}$ is:$\frac{ \partial u } {\partial x}- i \frac{ \partial u}{\partial y}$$\frac{ \partial u } {...
Arjun
1.2k
views
Arjun
asked
Dec 7, 2018
Others
nielit-2018
non-gate
differentiation
partial-order
+
–
0
votes
0
answers
64
ISI2017-PCB-A-4
Let $\lceil x \rfloor$ denote the integer nearest to $x$. For example, $\lceil 1.1 \rfloor =1, \lceil 1.5 \rfloor =1$ and $\lceil 1.6 \rfloor$ =2. Draw the graph of the function $y= \mid x - \lceil x \rfloor \mid$ for $0 \leq x \leq 4$. Find all the points $x, \: 0 \leq x \leq 4$, where the function is not differentiable. Justify your answer.
Let $\lceil x \rfloor$ denote the integer nearest to $x$. For example, $\lceil 1.1 \rfloor =1, \lceil 1.5 \rfloor =1$ and $\lceil 1.6 \rfloor$ =2. Draw the graph of the f...
go_editor
226
views
go_editor
asked
Sep 19, 2018
Calculus
isi2017-pcb-a
differentiation
+
–
0
votes
0
answers
65
ISI2017-MMA-13
An even function $f(x)$ has left derivative $5$ at $x=0$. Then the right derivative of $f(x)$ at $x=0$ need not exist the right derivative of $f(x)$ at $x=0$ exists and is equal to $5$ the right derivative of $f(x)$ at $x=0$ exists and equal to $-5$ none of the above is necessarily true
An even function $f(x)$ has left derivative $5$ at $x=0$. Thenthe right derivative of $f(x)$ at $x=0$ need not existthe right derivative of $f(x)$ at $x=0$ exists and is ...
go_editor
439
views
go_editor
asked
Sep 15, 2018
Quantitative Aptitude
isi2017-mma
engineering-mathematics
calculus
differentiation
+
–
2
votes
2
answers
66
ISI2016-MMA-8
Let $g: \mathbb{R} \rightarrow \mathbb{R}$ be differentiable with $g'(x^2)=x^3$ for all $x>0$ and $g(1) =1$. Then $g(4)$ equals $64/5$ $32/5$ $37/5$ $67/5$
Let $g: \mathbb{R} \rightarrow \mathbb{R}$ be differentiable with $g'(x^2)=x^3$ for all $x>0$ and $g(1) =1$. Then $g(4)$ equals$64/5$$32/5$$37/5$$67/5$
go_editor
822
views
go_editor
asked
Sep 13, 2018
Calculus
isi2016-mmamma
calculus
differentiation
+
–
0
votes
1
answer
67
ISI2016-MMA-24
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a strictly increasing function. Then which one the following is always true? The limits $\lim_{x \rightarrow a+} f(x) $ and $\lim_{x \rightarrow a-} f(x)$ exist for all real numbers $a$ If $f$ is differentiable at $a$ then ... such that $f(x)<B$ for all real $x$ There cannot be any real number $L$ such that $f(x)>L$ for all real $x$
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a strictly increasing function. Then which one the following is always true?The limits $\lim_{x \rightarrow a+} f(x) $ and $...
go_editor
474
views
go_editor
asked
Sep 13, 2018
Calculus
isi2016-mmamma
calculus
continuity
differentiation
limits
+
–
1
votes
0
answers
68
ISI2016-MMA-26
Let $x$ and $y$ be real numbers satisfying $9x^2+16y^2=1$. Then $(x+y)$ is maximum when $y=9x/16$ $y=-9x/16$ $y=4x/3$ $y=-4x/3$
Let $x$ and $y$ be real numbers satisfying $9x^2+16y^2=1$. Then $(x+y)$ is maximum when$y=9x/16$$y=-9x/16$$y=4x/3$$y=-4x/3$
go_editor
230
views
go_editor
asked
Sep 13, 2018
Others
isi2016-mma
differentiation
non-gate
+
–
2
votes
3
answers
69
ISI2016-MMA-27
Consider the function $f(x) = \dfrac{e^{- \mid x \mid}}{\text{max}\{e^x, e^{-x}\}}, \: \: x \in \mathbb{R}$. Then $f$ is not continuous at some points $f$ is continuous everywhere, but not differentiable anywhere $f$ is continuous everywhere, but not differentiable at exactly one point $f$ is differentiable everywhere
Consider the function $f(x) = \dfrac{e^{- \mid x \mid}}{\text{max}\{e^x, e^{-x}\}}, \: \: x \in \mathbb{R}$. Then$f$ is not continuous at some points$f$ is continuous eve...
go_editor
528
views
go_editor
asked
Sep 13, 2018
Calculus
isi2016-mmamma
calculus
continuity
differentiation
+
–
0
votes
0
answers
70
Differentiable
Why is a function not differentiable at x=k when f'(x) limits to infinity? Limit can be infinite too?
Why is a function not differentiable at x=k when f'(x) limits to infinity? Limit can be infinite too?
bts
385
views
bts
asked
Jun 25, 2018
Mathematical Logic
calculus
differentiation
continuity
engineering-mathematics
+
–
3
votes
3
answers
71
ISI2017-MMA-13
An even function $f(x)$ has left derivative $5$ at $x=0$. Then the right derivative of $f(x)$ at $x=0$ need not exist the right derivative of $f(x)$ at $x=0$ exists and is equal to $5$ the right derivative of $f(x)$ at $x=0$ exists and is equal to $-5$ none of the above is necessarily true
An even function $f(x)$ has left derivative $5$ at $x=0$. Thenthe right derivative of $f(x)$ at $x=0$ need not existthe right derivative of $f(x)$ at $x=0$ exists and is ...
jjayantamahata
2.0k
views
jjayantamahata
asked
Mar 27, 2018
Calculus
isi2017-mma
engineering-mathematics
calculus
differentiation
+
–
3
votes
1
answer
72
Mathematics GATE 2018 EE: 11
Let $f$ be a real-valued function of a real variable defined as $f(x) = x^{2}$ for $x\geq0$ and $f(x) = -x^{2}$ for $x < 0$.Which one of the following statements is true? $f(x) \text{is discontinuous at x = 0}$ ... $f(x) \text{is differentiable but its first derivative is not differentiable at x = 0} $
Let $f$ be a real-valued function of a real variable defined as $f(x) = x^{2}$ for $x\geq0$ and $f(x) = -x^{2}$ for $x < 0$.Which one of the following statements is true...
Lakshman Bhaiya
3.0k
views
Lakshman Bhaiya
asked
Feb 21, 2018
Calculus
gate2018-ee
engineering-mathematics
calculus
continuity
differentiation
+
–
2
votes
1
answer
73
MadeEasy Test Series: Calculus - Differentiability
At the point x = 1, the function
At the point x = 1, the function
Kuldeep Pal
532
views
Kuldeep Pal
asked
Jan 6, 2018
Calculus
made-easy-test-series
calculus
differentiation
continuity
+
–
3
votes
1
answer
74
TIFR CSE 2018 | Part A | Question: 5
Which of the following is the derivative of $f(x)=x^{x}$ when $x>0$ ? $x^{x}$ $x^{x} \ln \;x$ $x^{x}+x^{x}\ln\;x$ $(x^{x}) (x^{x}\ln\;x)$ $\text{None of the above; function is not differentiable for }x>0$
Which of the following is the derivative of $f(x)=x^{x}$ when $x>0$ ?$x^{x}$$x^{x} \ln \;x$$x^{x}+x^{x}\ln\;x$$(x^{x}) (x^{x}\ln\;x)$$\text{None of the above; function is...
Arjun
1.3k
views
Arjun
asked
Dec 10, 2017
Calculus
tifr2018
calculus
differentiation
+
–
0
votes
0
answers
75
Calculus
#Calculus Let f(x)= |x|^3/2, x€R then A.f is uniformly continuous B.f is Continous but not differentiable ar x=0 C. f is differentiable and f' is continuous D. f is differentiable but f' is discontinuous at x=0 What is the answer and how to ... kind of questions? My Answer is option D , I want to confirm if my reasoning to this question is correct as im learning calculus now.
#CalculusLet f(x)= |x|^3/2, x€R thenA.f is uniformly continuousB.f is Continous but not differentiable ar x=0C. f is differentiable and f' is continuousD. f is differen...
MancunianDevil
843
views
MancunianDevil
asked
Apr 19, 2017
Calculus
calculus
imits
continuity
differentiation
+
–
3
votes
0
answers
76
differentiable
The function is defined as follows. Which of the following is true? (A) f is discontinuous at all (B) f is continuous only at x = 0 and differentiable only at x = 0. (C) f is continuous only at x=0 and non differentiable at all (D) f is continuous at all and non differentiable at all
The function is defined as follows.Which of the following is true?(A) f is discontinuous at all(B) f is continuous only at x = 0 and differentiable only at x = 0.(C) f ...
firki lama
699
views
firki lama
asked
Mar 1, 2017
Calculus
differentiation
continuity
calculus
+
–
1
votes
2
answers
77
ISRO2012-ECE Engineering Mathematics
$1-x$ $(1-x)/x$ $1/x$ $x/(1-x)$
$1-x$$(1-x)/x$$1/x$$x/(1-x)$
sh!va
504
views
sh!va
asked
Feb 28, 2017
Calculus
engineering-mathematics
isro2012-ece
isro-ece
calculus
differentiation
+
–
27
votes
2
answers
78
GATE CSE 2017 Set 2 | Question: 10
If $f(x) = R \: \sin ( \frac{\pi x}{2}) + S, f’\left(\frac{1}{2}\right) = \sqrt{2}$ and $\int_0^1 f(x) dx = \frac{2R}{\pi}$, then the constants $R$ and $S$ are $\frac{2}{\pi}$ and $\frac{16}{\pi}$ $\frac{2}{\pi}$ and 0 $\frac{4}{\pi}$ and 0 $\frac{4}{\pi}$ and $\frac{16}{\pi}$
If $f(x) = R \: \sin ( \frac{\pi x}{2}) + S, f’\left(\frac{1}{2}\right) = \sqrt{2}$ and $\int_0^1 f(x) dx = \frac{2R}{\pi}$, then the constants $R$ and $S$ are$\frac{2}...
Madhav
8.5k
views
Madhav
asked
Feb 14, 2017
Calculus
gatecse-2017-set2
engineering-mathematics
calculus
differentiation
+
–
15
votes
2
answers
79
TIFR CSE 2017 | Part A | Question: 9
Consider the $majority$ function on three bits, $\textbf{maj}: \{0, 1\}^3 \rightarrow \{0, 1\}$ where $\textbf{maj}(x_1, x_2, x_3)=1$ if and only if $x_1+x_2+x_3 \geq 2$. Let $p(\alpha)$ be the probability that the output is $1$ when each input is set to ... $3 \alpha$ $\alpha^2$ $6\alpha(1-\alpha)$ $3\alpha^2 (1-\alpha)$ $6\alpha(1-\alpha)+\alpha^2$
Consider the $majority$ function on three bits, $\textbf{maj}: \{0, 1\}^3 \rightarrow \{0, 1\}$ where $\textbf{maj}(x_1, x_2, x_3)=1$ if and only if $x_1+x_2+x_3 \geq 2$....
go_editor
1.3k
views
go_editor
asked
Dec 21, 2016
Probability
tifr2017
probability
independent-events
differentiation
+
–
0
votes
1
answer
80
Diffrentiability+Limits
how to solve diffrentiability with standard procedure of f(a+h).
how to solve diffrentiability with standard procedure of f(a+h).
Rahul Jain25
684
views
Rahul Jain25
asked
Dec 9, 2016
Calculus
calculus
engineering-mathematics
differentiation
+
–
5
votes
1
answer
81
ISRO2011-59
$n$-th derivative of $x^n$ is $nx^{n-1}$ $n^n.n!$ $nx^n!$ $n!$
$n$-th derivative of $x^n$ is$nx^{n-1}$$n^n.n!$$nx^n!$$n!$
go_editor
2.0k
views
go_editor
asked
Jun 23, 2016
Calculus
isro2011
calculus
differentiation
+
–
36
votes
5
answers
82
GATE CSE 2016 Set 2 | Question: 02
Let $f(x)$ be a polynomial and $g(x)=f'(x)$ be its derivative. If the degree of $(f(x)+f(-x))$ is $10$, then the degree of $(g(x) - g(-x))$ is __________.
Let $f(x)$ be a polynomial and $g(x)=f'(x)$ be its derivative. If the degree of $(f(x)+f(-x))$ is $10$, then the degree of $(g(x) - g(-x))$ is __________.
Akash Kanase
10.4k
views
Akash Kanase
asked
Feb 12, 2016
Calculus
gatecse-2016-set2
calculus
normal
numerical-answers
differentiation
+
–
2
votes
1
answer
83
MadeEasy Test Series: Calculus - Differentiability
Q.64 A function f (x) is differentiated twice such that its differential equation λ2f (x) – 2λf ′(x) + f ′′(x) = 0 provides two equal value of λ for all x. It f (0) = 1, f′(0) = 2, then f(x) at x = 1 will be _________. Given ans -> 7.39 (7.00 - 7.80)
Q.64A function f (x) is differentiated twice such that its differential equation λ2f (x) – 2λf ′(x) + f ′′(x) = 0 provides two equal value of λ for all x. It f...
Akash Kanase
480
views
Akash Kanase
asked
Dec 19, 2015
Calculus
made-easy-test-series
calculus
differentiation
+
–
3
votes
1
answer
84
TIFR-2015-Maths-A-5
Let $f : \mathbb{R} \rightarrow \mathbb{R}$ denote the function defined by $f(x)= (1-x^{2})^{\frac{3}{2}}$ if $|x| < 1$, and $f(x)=0$ if $|x| \geq 1$. Which of the following statements is correct ? $f$ is not continuous $f$ is continuous but not differentiable $f$ is differentiable but $f'$ is not continuous. $f$ is differentiable and $f'$ is continuous.
Let $f : \mathbb{R} \rightarrow \mathbb{R}$ denote the function defined by $f(x)= (1-x^{2})^{\frac{3}{2}}$ if $|x| < 1$, and $f(x)=0$ if $|x| \geq 1$. Which of the follow...
makhdoom ghaya
563
views
makhdoom ghaya
asked
Dec 19, 2015
Calculus
tifrmaths2015
continuity
differentiation
+
–
2
votes
1
answer
85
TIFR-2014-Maths-A-3
Let $f: \mathbb{R} \to \mathbb{R}$ be a differentiable function such that $\displaystyle \lim_{x \to +\infty} f'(x)=1$, then $f$ is bounded $f$ is increasing $f$ is unbounded $f'$ is bounded
Let $f: \mathbb{R} \to \mathbb{R}$ be a differentiable function such that $\displaystyle \lim_{x \to +\infty} f'(x)=1$, then$f$ is bounded $f$ is increasing $f$ is unboun...
makhdoom ghaya
658
views
makhdoom ghaya
asked
Dec 10, 2015
Calculus
tifrmaths2014
differentiation
+
–
1
votes
1
answer
86
TIFR-2011-Maths-A-19
The derivative of the function $\int_{0}^{\sqrt{x}} e^{-t^{2}}dt$ at $x = 1$ is $e^{-1}$ .
The derivative of the function$\int_{0}^{\sqrt{x}} e^{-t^{2}}dt$at $x = 1$ is $e^{-1}$ .
makhdoom ghaya
575
views
makhdoom ghaya
asked
Dec 9, 2015
Calculus
tifrmaths2011
calculus
differentiation
+
–
1
votes
1
answer
87
TIFR-2011-Maths-A-9
The function $f(x)$ defined by $f(x) = \begin{cases} ax+b & \text{x ≥ 1 } \\ x^{2}+3x+3& \text{x ≤ 1} \end{cases}$ is differentiable For a unique value of a and infinitely many values of $b$ For a unique value of $b$ and infinitely many values of $a$ For infinitely many values of $a$ and $b$ None of the above
The function $f(x)$ defined by $f(x)= \begin{cases}ax+b & \text{x ≥ 1 } \\ x^{2}+3x+3& \text{x ≤ 1} \end{cases}$is differentiable For a unique value of a and infini...
makhdoom ghaya
517
views
makhdoom ghaya
asked
Dec 9, 2015
Calculus
tifrmaths2011
differentiation
+
–
2
votes
1
answer
88
TIFR-2011-Maths-A-5
The differential equation $\frac{dy}{dx}= y^{1/3}, y(0)=0$ has A unique solution No nontrivial solution Finite number of solutions Infinite number of solutions
The differential equation$\frac{dy}{dx}= y^{1/3}, y(0)=0$ hasA unique solutionNo nontrivial solution Finite number of solutionsInfinite number of solutions
makhdoom ghaya
452
views
makhdoom ghaya
asked
Dec 9, 2015
Calculus
tifrmaths2011
differentiation
non-gate
+
–
4
votes
4
answers
89
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
+
–
27
votes
2
answers
90
GATE CSE 1996 | Question: 3
Let $f$ be a function defined by $f(x) = \begin{cases} x^2 &\text{ for }x \leq 1\\ ax^2+bx+c &\text{ for } 1 < x \leq 2 \\ x+d &\text{ for } x>2 \end{cases}$ Find the values for the constants $a$, $b$, $c$ and $d$ so that $f$ is continuous and differentiable everywhere on the real line.
Let $f$ be a function defined by$$f(x) = \begin{cases} x^2 &\text{ for }x \leq 1\\ ax^2+bx+c &\text{ for } 1 < x \leq 2 \\ x+d &\text{ for } x>2 \end{cases}$$Find the va...
Kathleen
5.2k
views
Kathleen
asked
Oct 9, 2014
Calculus
gate1996
calculus
continuity
differentiation
normal
descriptive
+
–
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