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

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

Let f(x)=a^(x)-x ln a,a>1. Then the complete set of real values of x for which f'(x)>0 is

If f(x) = ((a+x)^(2)sin(a+x)-a^(2)sin a)/(x) , x !=0 , then the value of f(0) so that f is continuous at x = 0 is

If f(x) = ((a+x)^(2)sin(a+x)-a^(2)sin a)/(x) , x !=0 , then the value of f(0) so that f is continuous at x = 0 is

If f(x)=[(3sin x)/(x)],x!=0, then the value of f(0) so that the function f(x) is continuous at x=0 is

if f(x)=x^2sin(1/x) , x!=0 then the value of the function f at x=0 so that the function is continuous at x=0

if f(x)=x^2sin(1/x) , x!=0 then the value of the function f at x=0 so that the function is continuous at x=0

Let f(x) = |x| cos (1/x) for x ne 0 . Write the down the value of (f) (0) if f is continuous at x = 0

Let f (x)= {{:(x ^(n) (sin ""(1)/(x )",") , x ne 0),( 0"," , x =0):} Such that f (x) is continuous at x =0, f '(0) is real and finlte, and lim _(x to 0^(+)) f'(x) does not exist. The holds true for which of the following values of n ?

Let f (x)= {{:(x ^(n) (sin ""(1)/(x )",") , x ne 0),( 0"," , x =0):} Such that f (x) is continuous at x =0, f '(0) is real and finite, and lim _(x to 0^(+)) f'(x) does not exist. The holds true for which of the following values of n ?