Show that limit of sqrt(x){sqrt(x+2)-sqrt(x)}=1√x{√x+2−√x}=1 as x approaches to infinity?
1 Answer
Dec 8, 2017
Use a conjugate to rewrite the expression.
= (2sqrtx)/(sqrt(x+2)+sqrt(x))
Now the limit has indeterminate form
= (cancel(sqrtx)(2))/(cancel(sqrtx)(sqrt(1+2/sqrtx)+1))
The limit as