The concentration of a certain drug (in mg/cm3) in a patient's bloodstream t hr after injection is given by the following function.
C(t) = (0.6 t)/(t^2 + 5)
Evaluate the limit. (If an answer does not exist, enter DNE.)
lim(t->∞) (0.6t) / (t^2 + 5)
To evaluate this limit, we can divide both the numerator and denominator by t:
lim(t->∞) (0.6) / (t + 5/t)
Now as t approaches infinity, the term 5/t approaches 0. Therefore, the expression becomes:
lim(t->∞) (0.6) / (t)
Now as t approaches infinity, the entire expression approaches 0:
lim(t->∞) (0.6) / (t) = 0
To evaluate the limit of the function C(t), we can use the limit definition. Let's calculate the limit as t approaches a specific value, say "a".
The limit of C(t) as t approaches a is denoted as:
lim (t->a) C(t)
To find the limit, we substitute "a" into the function C(t):
lim (t->a) (0.6 t)/(t^2 + 5) = (0.6 a)/(a^2 + 5)
Therefore, the limit of the function C(t) as t approaches "a" is (0.6 a)/(a^2 + 5).
To evaluate the limit of the function C(t) as t approaches a certain value, we substitute that value into the function and see what the result is.
In this case, we need to evaluate the limit of C(t) as t approaches some value. Since you didn't specify which value t is approaching, I will assume we need to evaluate the limit as t approaches infinity.
To do that, we substitute infinity into the function and see what the result is:
C(t) = (0.6t)/(t^2 + 5)
As t approaches infinity, the term t^2 becomes dominant compared to the constant 5. So we can simplify the function as follows:
C(t) ≈ (0.6t)/(t^2)
Now we can cancel out one of the t's from the numerator and denominator:
C(t) ≈ 0.6/t
As t approaches infinity, 0.6/t approaches 0. Therefore, the limit of C(t) as t approaches infinity is 0.
So, the answer to the given limit is 0.