If the function f(x) defined by {:(f(x...

If the function f(x) defined by
`{:(f(x),=x sin(1/x),",","for"x != 0),(,=k, ",","for"x = 0):}` is continuous at x = 0, then k =

A

(a) `0`

B

(b) `1`

C

(c) `-1`

D

(d) `1/2`

Verified by Experts

The correct Answer is:

A

Similar Questions

Explore conceptually related problems

For what value of k, the function defined by {:(f(x),=(log(1+2x)sinx^(0))/(x^(2)),",","for" x != 0),(,=k, ",","for"x = 0):} is continuous at x = 0?

If {:(f(x),=((4x+1)/(1-4x))^(1/x),",",x != 0),(,=k, ",",x = 0):} is continuous at x = 0, then k =

{:(f(x),=(log(1+kx))/(sin x),",",x != 0),(,=5, ",",x = 0):} If f is continuous at x = 0, then k =

If {:(f(x),=(log)(sec^2x)^(cot^2x),",","for"x != 0),(,=k, ",","for"x = 0):} is continuous at x = 0 then k is

If f(x) = {((1-cosx)/x, ",", x != 0),(k, ",", x = 0):} is continuous at x = 0 then k =

f:R->R is defined by {:(f(x),=(cos3x-cosx)/(x^2),",","for" x != 0),(,=k, ",","for" x = 0):} If f(x) is continuous at x = 0, the value of k is

If {:(f(x),=(sec^2x)^(cot^2x),",",x != 0),(,=k, ",",x = 0):} is continuous at x = 0 , then k is equal to

If {:(f(x),=((e^(kx)-1)^(2)sinx)/(x^(3)),",",x != 0),(,=4, ",",x = 0):} is continuous at x = 0, then k =

If {:(f(x),=log_(1-3x)(1+3x),",",x != 0),(,=k, ",",x = 0):} is continuous at x = 0, then the value of k is