   Chapter 2.4, Problem 84E

Chapter
Section
Textbook Problem

Concentration of a Dreg in the Bloodstream The concentration of a certain drag in a patient’s bloodstream t hr after injection is given by C ( t ) = 0.2 t t 2 + 1 mg/cm3. Evaluate lim x → ∞ C ( t ) and interpret your result.

To determine

To evaluate: The value of limtC(t) and interpret the result.

Explanation

Given information:

The given function is,

C(t)=0.2tt2+1

Where,

•   C(t) is the concentration of certain drug in mg/cm3 .
•  t is time in hour.

Calculation:

As x approaches infinity, the limit of numerator and denominator of the function do not exist.

To evaluate limtC(t) , divide numerator and denominator of the given function by t2 and simplify it.

limtC(t)=limt0.2t1+1t2=limt0.2tlimt(1+1t2) (limxf(x)g(x)=limxf(x)limxg(x))=limt0

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