info@clay6.com
+91-9566306857
(or)
+91-9176170648
Ask Questions, Get Answers
Menu
X
JEEMAIN Crash Practice
15 Test Series
NEET Crash Practice
15 Test Series
JEEMAIN
Math
Physics
Chemistry
Practice Test Series
NEET
Physics
Chemistry
Biology - XII
Biology - XI
studyplans
JEEMAIN Crash Practice
15 Test Series
NEET Crash Practice
15 Test Series
JEEMAIN
Math
Physics
Chemistry
Practice Test Series
NEET
Physics
Chemistry
Biology - XII
Biology - XI
mobile
exams
ask
sample papers
tutors
pricing
login
X
ASK
Home
>>
JEEMAIN and NEET
>>
Mathematics
>>
Limit, Continuity and Differentiability
If $f$ is twice differentiable and $f''(0)=2$ then $\lim\limits_{x\to 0}\large\frac{2f(x)-3f(2x)+f(4x)}{x^2}$=
$(a)\;6\qquad(b)\;3\qquad(c)\;12\qquad(d)\;None\;of\;these$
jeemain
math
ch5
continuity-and-differentiability
differentiability
edium
q126
Share
asked
Jan 2, 2014
by
sreemathi.v
retagged
Jul 31, 2014
by
vijayalakshmi.r
Please
log in
or
register
to add a comment.
Please
log in
or
register
to answer this question.
1 Answer
limit=$\lim\limits_{x\to 0}\large\frac{2f'(x)-6f'(2x)+4f'(4x)}{2x}$
$\Rightarrow \lim\limits_{x\to 0}\large\frac{2f''(x)-12f''(2x)+16f''(4x)}{2}$
$\Rightarrow \large\frac{6f''(0)}{2}$
$\Rightarrow 6$
Hence (a) is the correct answer.
answered
Jan 2, 2014
by
sreemathi.v
Please
log in
or
register
to add a comment.
Related questions
If function $f(x)$ is differentiable at $x=a$ then $\lim\limits_{x\to a}\large\frac{x^2f(a)-a^2f(x)}{x-a}$ is
jeemain
math
class12
ch5
continuity-and-differentiability
differentiability
easy
q29
asked
Dec 23, 2013
by
sreemathi.v
1
answer
If $(x)$ is differentiable and strictly increasing function then the value of $\lim\limits_{x\to 0}\large\frac{f(x^2)-f(x)}{f(x)-f(0)}$ is
jeemain
math
class12
ch5
continuity-and-differentiability
differentiability
easy
q15
asked
Dec 20, 2013
by
sreemathi.v
1
answer
If $f$ is a real valued differentiable function satisfying $\mid f(x)-f(y)\mid\leq (x-y)^2,x,y\in R$ and $f(0)=0$ then $f(1)$ equals
jeemain
math
ch5
continuity-and-differentiability
differentiability
medium
q112
asked
Dec 31, 2013
by
sreemathi.v
1
answer
Let $f:R\rightarrow R$ be a differentiable function and $f(1)=4$, then the value of $\large \int_4^{f(x)}\large\frac{2t\;dt}{x-1}$ is
jeemain
math
ch5
continuity-and-differentiability
differentiability
medium
q104
asked
Dec 31, 2013
by
sreemathi.v
1
answer
$f(x)$ and $g(x)$ are two differentiable function on [0,2] such that $f''(x)-g''(x)=0$. $f'(1)=2g'(1)=4f(2)=3g(2)=9$ then $f(x)-g(x)$ at $x=\large\frac{3}{2}$ is
jeemain
math
ch5
continuity-and-differentiability
differentiability
medium
q110
asked
Dec 31, 2013
by
sreemathi.v
1
answer
Let $f:R\rightarrow R$ be a function such that $f(x+y)=f(x)+f(y)\forall x,y\in R$ if $f(x)$ is differentiable at $x=0$ then
jeemain
math
ch5
continuity-and-differentiability
differentiability
medium
q115
asked
Dec 31, 2013
by
sreemathi.v
1
answer
Let $f:R\rightarrow R$ be a differentiable function having $f(2)=6,f'(2)=\large\frac{1}{48}$.Then $\lim\limits_{x\to 2}\int_6^{f(x)}\large\frac{4t^3dt}{x-2}$ equals
jeemain
math
class12
ch5
limits-and-derivatives
differentiability
easy
q54
asked
Dec 24, 2013
by
sreemathi.v
1
answer
Ask Question
Tag:
Math
Phy
Chem
Bio
Other
SUBMIT QUESTION
►
Please Wait
Take Test
JEEMAIN Crash Practice
15 Test Series
NEET Crash Practice
15 Test Series
JEEMAIN
350+ TESTS
NEET
320+ TESTS
...
close