If the following function f(x) is continuous at x = 0, find the value of 'a':
`f(x) = {:{((1-cos4x)/x2,x<0),(a,x=0),((sqrtx/(sqrt(16+sqrtx)-4,x>0):}`

Determine k, if the following function is continuous at x = 0 f(x) = {{:((1 - cos 2x)/(2x^2)"," ,x != 0),(k",", x = 0):}

(i) Given f(x)={((1-cos4x)/(x^(2))" , "xne0),(k" , "x=0):} If f(x) is continuous at x=0, find the value of k. (ii) Given f(x)={((1-cos4x)/(8x^(2))" , "xne0),(k" , "x=0):} If f(x) is continuous at x=0, find the value of k.

Prove that the function f(x) = x + |x| is continuous at x = 0 .

Show that the following function is continuous at x = 0: f(x) = x sin1.x, when x ne 0 f(0) = 0.

Determine value of k so that the following function f(x) is continuous at x = 0. f(x) ={((sin 5x)/(3x)),(k):}, ((x ne 0),(x =0))

For what value of k, function f (x) is continuous at x = 0 where f(x) ={((1-cos 4x)/(x^2)),(k):}, ((x ne 0),(x =0))

For what value of k, function f (x) is continuous at x = 0 where f(x) ={((1-cos 4x)/(8x^2)),(k):}, ((x ne 0),(x =0))

For what value of k, function f (x) is continuous at x = 0 where f(x) ={((1-cos x)/(x^2)),(k):}, ((x ne 0),(x =0))

Determine, k if the following function is continuous at x = 0 f(x) = {{:((sin 3x)/(4x), x != 0),(k,x = 0):}

(a) Determine the value of k so that the following function f(x) is continous at x=0 f(x)={((sin2x)/(x)" , if "xne0),(k" , if "x=0):} (b) Determine k, if the following function is continuous at x=0: f(x)={((sin3x)/(4x)" , "xne0),(k" , "x=0):} (c) Determine k so that the following function f(x) is continuous at x=0 f(x)={((sin5x)/(3x)" , "xne0),(k" , "x=0):}