Find the value of a for which
`f(x)={((1-cos4x)/(8x^2), "" xne0),(a, x=0 ""):}` is continuous at x = 0

Find the value of a for which f(x)={(sin^2(ax)/(x^2), "" xne0),(1, x=0 ""):} is continuous at x = 0

Find the value of k for which f(x)={((kcosx)/(pi-2x), "" xnepi/2),(3",", ""x=pi/2):} is continuous at x=1

Find the value of k for which f(x)={(2x+k,0lexle 1),(3x, x>1):}, "" is continuous at x=1

Find the value of the k if the function f(x)={(kx^2, x ge 1),(4, x<1):} is continuous at x =1

Show that f (x) = f(x) = {(x,sinfrac(1)(x)),(0,x=0):} is continuous at x = 0

Prove that f (x) =|x| is continuous at x =0

If the function f(x)={{:((sin x)/(x) + cos x", if " x ne 0 ), (k", if " x =0 ):} is continuous at x=0, then find the value of k.

Find the domain and range of f if . f(x)=(x+2)/(x^2-8x-4)