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 a for which f(x)={((1-cos4x)/(8x^2), "" xne0),(a, 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

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

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

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.

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

Find the value of a and b if f(x) = {(3ax+b,x>1),(11,x=1),(5ax-2b,x<1):} is continuous at x = 1

Find the value of a for which the function f(x) = a sin x + (1)/3 sin 3x has an extremum at x =pi/3 .

If f (x) = f(x)={(x^2sin, 1/x,x ne0),(0, x=0, ):} Show that f is differentiable and continuous at x=0