f(x)={[x sin(1)/(x),,x!=0],[0,,x=0]" is continuous at "x=0

Show that function f(x) given by f(x)={(x sin(1/x),,,x ne 0),(0,,,x=0):} is continuous at x=0

If f(x)={{:("x sin"(1)/(x)",",xne0),(k",",x=0):} is continuous at x=0, then the value of k is

Prove that f(x)={(sin x)/(x);x!=0 and 1;x=0. is continuous at x=0

A function f(x) is defined as follows f(x)={(sin x)/(x),x!=0 and 2,x=0 is,f(x) continuous at x=0? If not,redefine it so that it become continuous at x=0 .

Show that the function f(x)={x sin((1)/(x)) when x!=0;=0, when x=0 is continuous butnot differentiable at x=0

If f(x)={(x^(k) sin((1)/(x))",",x ne 0),(0",", x =0):} is continuous at x = 0, then

Show that f(x) = x sin ((1)/(x)), x ne 0 , f(0) = 0 is continuous at x = 0