If a function is continuous at x=a, then find
`lim_(hto0)+1/2{f(a+h)+f(a-h)}`

If a function f(x) = (x^2-4)/(x-2) is continuous at x = 2, then what is the value of f (2) ?

Show that the function f(x)=2x-|x| is continuous at x=0 .

If 'f(x)= {((1-cos4x)/(x^2)),whenx 0):} , and f is continuous at x=0, then find the value of k.

If the function f(x) = (sin 10x)/(x) is continuous at x = 0 then what is f(0)?

For what valueof K is the following function continuous at x = 2 ? f(x)={(2x+1,when x 2):}

Find the value of k so that the function f is continuous at x=pi//2,f(x)={:{((kcosx)/(pi-2x)", if "x!=(pi)/(2)),(5", if "x=(pi)/(2)):}

Evaluate the following lim_(hto0) ((x+h)^3-x^3)/h

If the function f(x) defined by f(x)={((log(1+ax)-log(1-bx))/(k)", if "x!=0),(" k, if "x=0):} is continuous at x=0 , then find the value of k.