If f(x)={((x^(3)+x^(2)-16x+20)/((x-2)^(...

If `f(x)={((x^(3)+x^(2)-16x+20)/((x-2)^(2))",",x ne 2),(k",", x =2):}` is continuous at x = 2, then the value of k is

A

2

B

5

C

7

D

3

Verified by Experts

The correct Answer is:

C

Similar Questions

Explore conceptually related problems

If f(x) {:(=(x^(3)+x^2-16x+20)/((x-2)^(2)) ", if " x!= 2 ), (=k ", if " x = 2 ) :} is continuous at x = 2 , then

If f(x) = {(kx^(2),"if"x le 2),(3,"if" x gt 2):} is continuous at x = 2, then the value of k is

If f(x)={((sin 5x)/(x^(2)+2x)",", x ne 0),(k+(1)/(2)",", x =0):} is continuous at x = 0, then the value of k is

If f(x) = {{:((x^(2)-(a+2)x+2a)/(x-2)",",x ne 2),(" "2",",x = 2):} is continuous at x = 2, then a is equal to

If f(x) = {((x^6=1/64)/(x^3-1/8),",",x != 1/2),(k,",",x = 1/2):} is continuous at x = 1/2 , then the value of k is

For what value of k, f(x)={((2^(x+2)-16)/(4^(x)-16)",", x ne 2),(k",", x =2):} is continuous at x = 2?

If the function f(x)={((1-cosx)/(x^(2))",","for "x ne 0),(k,"for " x =0):} continuous at x = 0, then the value of k is

If f(x) = {((sin3x)/(x), x !=0),(k/2,x=0):} is continuous at x = 0, then the value of k is

If f(x) = {(2x+1,",",x le 1),(-3-kx^(2),",",x gt 1):} is continuous at x = 1, then the value of k is