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

Let f,g:R rarr R be two function diffinite f(x)={x sin((1)/(x)),x!=0; and 0,x=0 and g(x)=xf(x)

If f(x)={[(cos x)^((1)/(sin x)),,x!=0],[K,,x=0]} is differentiable at x=0 Then K=

Examine for continuity, each of the following functions: f(x) = {:{((x-a) sin (1/(x-a)), x ne a), (0, x = a):} at x = a

Discuss the continuity of f(x)={x^(2)sin((1)/(x)),quad x!=0quad 0,quad x= at x=0

If g(x)=xf(x), where f(x)={x sin((1)/(x));x!=00;x=0} then at x=0

Let f(x)={x^(p)sin((1)/(x))+x|x^(3)|,x!=0,0,x=0 the set of values of p for which f'(x) is continuous at x=0 is

Test for continuity of the following function at x=a:f(x)={(x- a) sin((1)/(x-a), where x!=a(x-a)0, when x=a

Prove that f(x)={x sin((1)/(x)),x!=0,0,x=0 is not differentiable at x=0

Show that the function f(x)={x^(m)sin((1)/(x))0,x!=0,x=0 is differentiable at x=0 if m>1 continuous but not differentiable at x=0, if 0.

A function f(x) is defined as follows : f(x)={(x^(2)"sin"(1)/(x)", if "x!=0),(0", if "x=0):} show that f(x) is differentiable at x=0.