N(t) = 100t / (t + 9)
where t >=0
Find lim x approaching to infinity N(t)
sorry, it's "t approaching to infinity"
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
To find the limit as t approaches infinity of N(t), we can analyze the behavior of the function N(t) as t gets larger and larger.
Let's first simplify the function N(t) by canceling out the common factor of t in the numerator and denominator:
N(t) = 100 / (1 + 9/t)
As t approaches infinity, we can see that 9/t approaches zero:
lim(t->∞) (9/t) = 0
Therefore, the function simplifies to:
N(t) = 100 / (1 + 0) = 100
Hence, the limit as t approaches infinity of N(t) is 100.