Question

Suppose  H(t)=√(3t+2)  What is the average rate of change of H(t) with respect to t as t changes from 2 to 2.01 ?

Answer 1

H(t)=√(3t+2)

H(2)=√8=2√2; H(2.01)=√8.03. 2.01-2=0.01.

Rate of change=(√8.03-√8)/0.01=0.005298338/0.01=0.5298 approx.

An approximation is:

√8.03=√(8(1+0.03/8))=(√8)(1+0.03/8)^½=(√8)(1+0.03/16)=(√8)(1.001875).

So √8.03-√8=0.001875√8, and (√8.03-√8)/0.01=0.1875√8=0.5303.