f:R->R is defined by f(x)={(cos3x-cosx)/...

`f:R->R` is defined by `f(x)={(cos3x-cosx)/(x^2), x!=0lambda, x=0` and `f` is continuous at `x=0;` then `lambda=`

A

-2

B

-4

C

-6

D

-8

Text Solution

Verified by Experts

The correct Answer is:

B

Topper's Solved these Questions

CONTINUITY
TARGET PUBLICATION|Exercise Competitive Thinking|63 Videos
CONTINUITY
TARGET PUBLICATION|Exercise Evaluation Test|10 Videos
CONTINUITY
TARGET PUBLICATION|Exercise Evaluation Test|10 Videos
BINOMIAL DISTRIBUTION
TARGET PUBLICATION|Exercise EVALUTION TEST|12 Videos
DEFINITE INTEGRALS
TARGET PUBLICATION|Exercise EVALUATIO TEST|30 Videos

Similar Questions

Explore conceptually related problems

f:R rarr R is defined by f(x)={(cos3x-cos x)/(x^(2)),x!=0 lambda,x=0 and f is continuous at x=0; then lambda=

If f(x)=(1-cos2x)/(x^(2))quad , x!=0 and f(x) is continuous at x=0 ,then f(0)=?

If f (x) {{:((1 - cos 8 x )/(x^(2)) "," x ge 0 ),(lambda ", " x lt 0 ) :} is continous at x = 0 than lambda = ?

A function f(x) is defined as below f(x)=(cos(sin x)-cos x)/(x^(2)),x!=0 and f(0)=a f(x) is continuous at x=0 if 'a' equals

Define f(0) such that the function f(x)=(cos(sin x)-cos x)/(x^(2)),x!=0, is continuous at x=0

if f(x)=(e^(x^(2))-cosx)/(x^(2)) , for xne0 is continuous at x=0 , then value of f(0) is

If f: RR -> RR defined by f(x) = {(a^2cos^2x+x^2sin^2x;, x 0):} is continuous at x=0.

f(x)={[x]+[-x], where x!=2 and lambda where If f(x) is continuous at x=2 then,the value of lambda will be

Let f(x)={x^(2)|(cos)(pi)/(x)|,x!=0 and 0,x=0,x in R then f is

TARGET PUBLICATION-CONTINUITY-Critical Thinking

For what value of k, function f(x)={((k cosx)/(pi-2x)",","if "x ne (pi...
Text Solution
|
If {:(f(x),=(cos x - sin x)/(cos 2x),",", x != (pi)/4),(,=k, ",", x = ...
Text Solution
|
f:R->R is defined by f(x)={(cos3x-cosx)/(x^2), x!=0lambda, x=0 and f ...
Text Solution
|
If f(x) is continuous at x=pi/4, where f(x)=(1-tanx)/(1-sqrt(2)sin x),...
Text Solution
|
If f(x) ={((3sinx-sqrt(3)cosx)/(6x-pi),",",x != (pi)/6),(a, ",",x = pi...
Text Solution
|
If f(x)=(1-sinx)/((pi-2x)^2),w h e nx!=pi/2a n df(pi/2)=lambda, the f(...
Text Solution
|
If f(x) = ((a+x)^(2)sin(a+x)-a^(2)sin a)/(x) , x !=0, then the value o...
Text Solution
|
If the function f(x)=(2-sqrt(x+4))/(sin2x)(x ne 0) is continuous at x ...
Text Solution
|
The value of f(0), so that the function f(x)=((27-2x)^2-3)/(9-3(243+5x...
Text Solution
|
If f(x) is continuous at x=pi/2, where f(x)=(sqrt(2)-sqrt(1+sin x))/(...
Text Solution
|
If f(x) = ((1+sinx)-sqrt(1-sinx))/(x) , x != 0, is continuous at x = 0...
Text Solution
|
If the function f(x) = (cos^(2)x - sin^(2)x-1)/(sqrt(x^(2)+1)-1), x !=...
Text Solution
|
The value of f at x =0 so that funcation f(x) = (2^(x) -2^(-x))/x , ...
Text Solution
|
If f(x)=(3^(x)+3^(-x)-2)/(x^(2)) for x ne 0 is continuous at x = 0, i...
Text Solution
|
If f(x) is continuous at x = 0, where {:(f(x),=(8^(x)-2^(x))/(k^(x)-1)...
Text Solution
|
If f(x) is continuous at x=0, where f(x)=((e^(3x)-1)sin x^(@))/(x^(2))...
Text Solution
|
If {:(f(x),=(e^(5x)-e^(2x))/(sin 3x),",",x != 0),(,=k/2, ",",x = 0):} ...
Text Solution
|
If f(x) = (e^(x)-e^(sinx))/(2(x sinx)) , x != 0 is continuous at x = 0...
Text Solution
|
In order that the function f(x)=(x+1)^(cotx) is continuous at x = 0, f...
Text Solution
|
If {:(f(x),=((4x+1)/(1-4x))^(1/x),",",x != 0),(,=k, ",",x = 0):} is...
Text Solution
|