In a biochemical assay

MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

In a biochemical assay, the instantaneous efficiency ratio of two reagents at time

t

seconds is modeled by

R(t)=\frac{e^{0.04t}-1-0.04t}{\ln(1+0.02t)-0.02t}.

(a) Demonstrate that

R(t)

is undefined by direct substitution at

t=0

. (b) Compute

\displaystyle \lim_{t\to 0}R(t)

and interpret the numerical value in terms of the comparative initial efficiencies of the two reagents. (c) Determine the smallest positive value of

t

(to three decimal places) for which

|R(t)-\lim_{t\to 0}R(t)|<0.001

. Clearly outline the reasoning used to obtain your estimate.