Question

How do you find the limit of `[sqrt(x+1) - 1]/[x]` as x approaches 0?

Answer 1

`1/2`

Explanation:

`[sqrt(x+1) - 1]/[x] = ((sqrt(x+1)-1)(sqrt(x+1)+1))/(x(sqrt(x+1)+1)=`
`(x+1-1)/(x(sqrt(x+1)+1)) = 1/(sqrt(x+1)+1)` so

`lim_(x->0)[sqrt(x+1) - 1]/[x] equiv lim_(x->0) 1/(sqrt(x+1)+1) = 1/2`