Determine the constant k(if it exists), so that the following functions may be continuous:
`f(x) = {:{(k(x^2 - 2x), x < 0),(cos x, x ge0):}`

Determine the constant k(if it exists), so that the following functions may be continuous: f(x) = {:{(kx^2, xle2),(3,x>2):}

Show that the following functions are continuous: f(x) = sin(x^2)

Show that the following functions are continuous: f(x) = cos(x^2)

Determine the value of k so that following functions are continuous at x = 0 f(x) = {{:((sin 2x)/(x)"," ,"if " x != 0),(k",","if " x = 0):}

Determine the constant lambda , so that the function is continuous at x=1 f(x) = {{:((x -1)/(x + 1)"," , " if " x != 1),(lambda - 1",", "if "x = 1):}

(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):}

Determine the constants 'a' and 'b' so that the function 'f' defined below is continuous everywhere: f(x) = {:{(x+2,xle2),(ax+b,2 < x<5),(3x-2,xge5):}

In the following, determine the constant so that given function is continuous at indicated point: f(x) ={:{((x^2-3x+2)/(x-1), if x ne1),(k, if x =1):} at x =1