Question

How do you find `lim sqrtt(sqrt(t+2)-sqrt(t+1))` as `t->oo`?

Answer 1

`1/2`

Explanation:

`sqrtt(sqrt(t+2)-sqrt(t+1))=sqrtt((t+2-(t+1)))/(sqrt(t+2)+sqrt(t+1))=`
`(sqrtt/sqrtt) 1/((sqrt(1+2/t)+sqrt(1-1/t)))=1/(sqrt(1+2/t)+sqrt(1+1/t))`

so

`lim_(t->oo)sqrtt(sqrt(t+2)-sqrt(t+1))=lim_(t->oo)1/(sqrt(1+2/t)+sqrt(1+1/t))=1/2`