If f(x) = (x-e^(x) + cos 2x)/(x^(2)), x ...

If `f(x) = (x-e^(x) + cos 2x)/(x^(2)), x ne 0` is continuous at x = 0, then

A

`f(0) =5//2`

B

`[f(0) ]=-2`

C

`{f(0) =0`

D

`[ f(0) ]{f(0)}=-1.5`

Verified by Experts

The correct Answer is:

D

Similar Questions

Explore conceptually related problems

If f(x)=(x-e^(x)+cos2x)/(x^(2)) where x!=0 , is continuous at x=0 then (where, {.} and [x] denotes the fractional part and greatest integer)

If f (x)= {{:((x-e ^(x)+1-(1-cos 2x))/(x ^(2)), x ne 0),(k,x=0):} is continous at x=0 then which of the following statement is false ?

Let the function f(x)=x^(2)sin((1)/(x)), AA x ne 0 is continuous at x = 0. Then, the vaue of the function at x = 0 is

If the function f(x)=(sin3x+a sin 2x+b)/(x^(3)), x ne 0 is continuous at x=0 and f(0)=K, AA K in R , then b-a is equal to

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

Let f(x) = (e^x x cosx-x log_e(1+x)-x)/x^2, x!=0. If f(x) is continuous at x = 0, then f(0) is equal to

If f(x)={{:((sinpix)/(5x)",",x ne0),(k,","0):} is continuous at x=0 , then k is equal to

The value of k for which f(x)= {((1-cos 2x )/(x^2 )", " x ne 0 ),(k ", "x=0):} continuous at x=0, is :

The value of the function f at x=0 so that the function f(x)=(2^(x)-2^(-x))/(x), x ne0 , is continuous at x=0 , is

If f(x)=(2x+3sinx)/(3x+2sinx) , x!=0 is continuous at x=0 , then find f(0)