Question

N(t) = 100t / (t + 9)
where t >=0

Find lim x approaching to infinity N(t)

Answer 1

sorry, it's "t approaching to infinity"

Answer 2

Use an intuitive approach and get a "feel" for large numbers,
suppose we use x = 100,000
we would have 10,000,000/100,001
= 99.99900001
would you agree that this is 100 for all practical purposes?
on your calculator try x = 1,000,000 , you will get even closer to 100

so the limit 100t/(t+9) as t ----> infinitiy = 100

or

by L' Hopital's Rule
lim 100t(t+9)
= limit 100/1 = 100