Question

based on you guy's knowledge of limits explain(without using algebra or tables) why the two functions: g(x)=(sqroot(100+x)-(sqroot(100-x))/x and
G(x)=(sqroot(100+x^n)-(sqroot(100+x^n))/x^n should have the same limit as x approaches 0

Answer 1

I guess its because as x approaches 0 , x^n also approaches 0
- though i'm not not absolutely sure about that

Answer 2

Because x^n -> 0 whenever x goes to zero for any n>0