The concentration of a certain drug (in mg/cm3) in a patient's bloodstream t hr after injection is given by the following function.

Question

C(t) = (0.6 t)/(t^2 + 5)
Evaluate the limit. (If an answer does not exist, enter DNE.)

Answer 1

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