Question

How do you find the limit `sqrtx/(x-1)` as `x->1^+`?

Answer 1

`= +oo`

Explanation:

If we let `x = 1 + delta`, where `0 < delta "<<" 1`

... then we can say that:

`lim_(x to 1^+) sqrtx/(x-1) = lim_(delta to 0) sqrt(1+ delta) /((1+ delta) -1)`

Expanding the numerator by the Binomial Expansion....

`=lim_(delta to 0) (1+ 1/2 delta + O(delta^2)) /(delta)`

`= lim_(delta to 0) 1/delta + 1/2 + O(delta) = +oo`