InterviewSolution
Saved Bookmarks
| 1. |
If f(x)=cos^(-1)(sgn((2[x])/(3x-[x]))), where sgn ( ) denotes the signum function and [.] dentoes the greatest integer functions, then which of the following is/are correct? |
|
Answer» `underset(xto1)(LIM)f(x)=0` `=underset(hto0)(lim)COS^(-1)(sgn((2)/(3+3h-1)))` `=underset(hto0)(lim)cos^(-1)(sgn((2)/(2+3h)))=0` `L.H.L=underset(hto0)(lim)f(1-h)=underset(hto0)(lim)` `cos^(-1)(sgn((0)/(3-3h)))=cos^(-1)(0)=(PI)/(2)` `becausef(x)` is discontinuous hence non-derivable at `x=1` `becausef^(')(-1^(+))=underset(hto0)(lim)(f(-1+h)-f(-1))/(h)=0` and `f^(')(-1^(-))=underset(hto0)(lim)(f(-1-h)-f(-1))/(h)=0` `impliesf^(')(-1^(+))=f^(')(-1^(-))=0` `becausef(x)` is derivable at `x=-1` |
|