Show that f (x) =`f(x) = {(x,sinfrac(1)(x)),(0,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

Prove that f (x) =|x| 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)={(2x+k,0lexle 1),(3x, x>1):}, "" is continuous at x=1

Prove that a rational function f given by f (x) = frac(P(x))(Q(x)),Q (x) ne 0 is continuous

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.

if f(xy) = f(x) f(y) for all x and y and if f(x) is continuous at x = 1, then show that it is continuous for all x except 0

Prove that f(x) = sin x and f(x) = cos x are continuous.

For what value of k, the function f given by f(x) = {(2x+1,x 2):} is continuous.

Examine the continuity of the following function at the given point : f(x) = {(1 + x, x 0),(1, x = 0):} at x = 0.