Question

How do you find `lim 1/sqrtx-1/x` as `x->0^+`?

Answer 1

Simplify the expression:

`1/sqrtx - 1/x = (x-sqrtx)/(xsqrtx) = (sqrtx-1)/x`

Passing to the limit:

`lim_(x->oo) (1/sqrtx - 1/x ) = lim_(x->oo) (sqrtx-1)/x = -1 xx +oo = -oo`