Find the value of k, if the functions are continuous at the points given against them :
`{:(f(x)=(1-coskx)/(x sin x)",","for" x ne0),(=9",","for" x=0):}}at x=0.`

Find the value of k, if the functions are continuous at the points given against them : {:(f(x)=(e^(kx)-1)/sinx",","for" x ne0),(=4",","for" x=0):}}at x=0.

Find the value of k, if the functions are continuous at the points given against them : {:(f(x)=x^(2)+1",", "for" x ge0),(=2sqrt(x^(2)+1)+k",","for" x lt0):}}at x=0.

Discuss the continuity of the following functions at the points shown against them : {:(f(x)=(x)/(|x|)",","for"x ne0),(=1",","for"x=0):}}at x=0.

Find the values of k so that the function f is continuous at the indicated point f(x) = {((1- cos (kx))/(x^(2))",","if " x ne 0),((1)/(2)",","if " x= 0):} at x= 0

f(x) = {{:((1-coskx)/(x sinx), if x ne 0),(1/2, if x = 0):} at x = 0

f(x) = {{:((1-coskx)/(x sinx), if x ne 0),(1/2, if x = 0):} at x = 0

f(x) = {{:((1-coskx)/(x sinx), if x ne 0),(1/2, if x = 0):} at x = 0

Discuss the continuity of the following functions at the points shown against them : {:(f(x)=(logx-log8)/(x-8)",","for"x ne0),(=10/7",","for"x=0):}}at x=8.

Discuss the continuity of the functions at the points given against them. If a function is discontinuous, determine whether the discontiunity is removable. In this case, redefine the function, so that it becomes continuous : {:(f(x)=(1-cos 3x)/(x tan x)",","for" x ne0),(=9",","for" x=0):}}at x=0.