If `f(x)={x^nsin(1/(x^2)),x!=0 0,x=0,(n in I),t h e n` `("lim")_(xvec0)f(x)e xi s t sforn >1` `("lim")_(xvec0)f(x)e xi s t sforn<0` `("lim")_(xvec0)f(x)` does not exist for any value of `n` `("lim")_(xvec0)f(x)` cannot be determined

Options

A. `(pi)/(2)`
B. `(pi)/(2sqrt(2))`
C. `(pi)/(sqrt(2))`
D. `sqrt(2)pi`

Answer

A, B

Explanation

For `ngt0, underset(xto0)limx^(n)sin(1//x^(2))=0xx(" any value between-1 to 1")=0`
For `nlt0,underset(xto0)limx^(n)sin(1//x^(2))=ooxx(" any value between-1 to 1")=+-oo`