Find the values of a and b so that the following function is continuous at x = 3 and x=5:
`f(x) = {:{(1, if xle3),(ax+b,if 3< x <5),(7, if 5lex):}`

Prove that the function f(x) = 5x-3 is continuous at 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):}

Find the values of k so that the function f is continuous at the indicated point : f(x)={(kx+1,,,, if x le5),(3x-5,,,, if x>5):} at x=5

Find the values of k so that the function f is continuous at the indicated point : f(x)={(kx+1,,,, if x lepi),(cosx,,,, if x>pi):} at x=pi

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 choice of a and b are the following functions continuous? f(x) = {:{(x^2, x le0),(ax+b,x>0):}

Find the values of k so that the function f is continuous at the indicated point : f(x)={(kcosx/(pi-2x),,,, if x ne pi/2),(3,,,, if x=pi/2):} at x=pi/2

For what choice of a and b are the following functions continuous? f(x) = {:{(ax^2 + b, x > 2),(2, x = 2),(2ax - b, x < 2):}

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):}

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