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

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Answer 1 · 2017-02-13T09:43:23

$1/2$

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

so

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

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