f(x)=x^(a)sin((1)/(x))x!=0

Let f(x)={x^(p)sin((1)/(x)),x!=0 and 0,x=0 and A and B are two sets such that A and B are continuous anddifferential of f(x) at x=0 respectively then find A nn B.

A function f(x) is defined as f(x)=[x^(m)(sin1)/(x),x!=0,m in N and 0, if x=0 The least value of m for which f'(x) is continuous at x=0 is

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

If f(x)=x sin((1)/(x)),x!=0 and f(x)=0,x=0 then show that f'(0) does not exist

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.

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

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

If f(x)={x^(2)sin((1)/(x^(2))),x!=0,k,x=0 is continuous at x=0, then the value of k is

Examine the differentiability of following function x=0,f(x)={e^(-(1)/(x^(2)))*sin((1)/(x))x!=0 and 0,x=0

g(x)=xf(x) , where f(x)=x"sin"(1)/(x),x!=0=0,x=0 . At x=0 :