Question

How do you find `lim (1-t/(t-1))/(1-sqrtt/(t-1))` as `t->oo` using l'Hospital's Rule?

Answer 1

`0`

Explanation:

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

then

`lim_(t->oo)(1-t/(t-1))/(1-sqrtt/(t-1)) = lim_(t->oo)-1/sqrtt(1/(sqrt t-1/sqrtt-1)) = 0`