Home
Class 12
MATHS
The function f(x)=((3^x-1)^2)/(sinx*ln(1...

The function `f(x)=((3^x-1)^2)/(sinx*ln(1+x)), x != 0,` is continuous at `x=0,` Then the value of `f(0)` is

A

`log_(e)3`

B

`2log_(e)3`

C

`(log_(e)3)^(2)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Since, f(x) to be continuous at x = 0.
`therefore lim_(x to 0)f(x)=f(0)`
`rArr lim_(x to 0)((3^(x)-1)^(2))/(xinx*log_(e)(1+x))=f(0)`
`rArr f(0)=lim_( x to 0) (((3^(x)-1)/(x))^(2))/((sinx)/(x)*(log_(e)(1+x))/(x))=((log_(e)3)^(2))/(1xx1)=(log_(e)3)^(2)`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2 (MISCELLANEOUS PROBLEMS)|60 Videos

  • CONTINUITY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|16 Videos

  • CIRCLE AND CONICS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise All Questions|74 Videos

  • DEFINITE INTEGRALS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|22 Videos

Similar Questions

Explore conceptually related problems

The function f(x)=((3^(x)-1)^(2))/(sin x*ln(1+x)),x!=0, is continuous at x=0, Then the value of f(0) is

If the function f(x)=((4^(sin x)-1)^(2))/(x*log(1+2x)) , for x!=0 is continuous at x=0 , find f(0) .

If the function f(x) = (x(e^(sinx) -1))/( 1 - cos x ) is continuous at x =0 then f(0)=

If f(x) = (e^(x)-e^(sinx))/(2(x sinx)) , x != 0 is continuous at x = 0, then f(0) =

The function f(x)={{:(sinx/x+cosx", if "xne0),(k", if "x=0):} is continuous at x = 0, then the value of 'k' is :

In order that the function f(x) = (x+1)^(cot x) is continuous at x=0 , the value of f(0) must be defined as :

If the function f(x)=((4^(sinx)-1)^(2))/(x log (1+2x)), "for" x ne0, is continous at x=0, find f(0).

If f(x) (2^(x)-1)/(1-3^(x)) , x != 0 is continuous at x = 0 then : f(0) =