The function `f(x)=x^(2)"sin"(1)/(x)`, `xne0,f(0)=0` at x=0

f(x)={(x^2 sin (1/x), xne0 ),(0, x=0):} at x=0

Which one of the following is correct in respect of the function f(x)=(x^(2))/(|x|) for xne0 and f(0)=0 ?

Consider the following statements in respect of the function f(x)=sin((1)/(x)) for xne0 and f(0)=0 1. underset(xrarr0)lim f(x) exists 2. f(x) is continuous at x = 0 Which of the above statements is/are correct?

The value of k for which the function f(x)={(sin(5x)/(3x)+cosx, xne0),(k, x=0):} is continuous at x=0 is

Test the continuity of the function f (x) : f(x)={{:(x^(2)sin.(1)/(x),"when " xne0),(0,"when " x=0):}

Conisder the function f(x)={{:(x^(2)ln|x|,xne0),(0,x=0):}. "What is" f'(0) equal to?

Show that the function f(x)={{:(x"cos"(1)/(x),"when"xne0),(0,"when"x=0):} is continuous at x=0.

Determine the value of constant A so that the function f(x)={((1-cosx)/(x^(2))" , "xne0),(A" , "x=0):} is continuous at x=0

Examine the continuity of the function f(x)={{:((|"sin"x|)/(x),"when " xne0),(" 1","when "x=0):}

A function f is defined as follows f(x)=x^(p)cos((1)/(x)),xne0 f(0)=0 What conditions should be imposed on p so that f may be continuous at x=0 ?