If the function f(x) = (x(e^(sinx) -1))/...

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

A

1

B

0

C

2

D

`(1)/(2)`

Verified by Experts

The correct Answer is:

C

`f(0)= lim_(x to 0) f(x) =lim_(x to 0) (x(e^(sinx)-1))/(1-cosx)`
`=lim_(x to 0) (e^(sinx)-1)/(sinx)*(sinx)/(x) *(x^(2))/(1-cosx)=2`

Similar Questions

Explore conceptually related problems

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

If the function f(x)=(e^(x^(2))-cos x)/(x^(2)) for x!=0 is continuous at x=0 then f(0)

If f(x) = ((1+sinx)-sqrt(1-sinx))/(x) , x != 0 , is continuous at x = 0, then f(0) is

If f(x) =(1+sin x - cos x)/(1-sin x - cos x ), x != 0 , is continuous at x = 0 , then f(0) = ………

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 :

For the function f(x) = (log_(e )(1+x)-log_(e )(1-x))/(x) to be continuous at x = 0, the value of f(0) should be

If function f(x) = (sqrt(1+x) - root(3)(1+x))/(x) is continuous function at x = 0, then f(0) is equal to

If f(x) = (1+sin x - cos x)/(1- sin x - cos x ) , x != 0 is continuous at x = 0 , then : f(0) =