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

Show that the following function are continuous at x=0: f(x) = |x|cos(1/x) for x ne0 f(0) = 0

Show that the following function are continuous at x=0: f(x) = {:{(xcos(1/x), when x ne0),(0,whenx=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))

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):}

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):}

Examine the following functions for continuity: f(x) = {:{(x^n sin1/x, x ne 0),(-, x= 0):} at x = 0, where n ge 1.

Examine the following functions for continuity: f(x) = {:{(x cos (1/x), x ne 0),(0, x = 0):} at x = 0

In the following, determine the constant so that given function is continuous at indicated point: f(x) ={:{((sin2x)/(5x), when x ne0),(m, when x=0):} at x =0

Examine the following functions for continuity: f(x) = {:{((x-|x|)/x, x ne 0),(2,x=0):} at x = 0