Rate of Change

**lisa1984wilson** · May 25th 2009, 06:10 AM

I need help with this..I have 50 of these problems so if you can show me how to calculate this one I can do the rest myself...Thanks!
Let s(t)=√t
a.Find the average rate of change of s(t) with respect to t as t changes from t=1 to t=1/4
b.Use calculus to find the instantaneous rate of change of s(t) at t=1 and compare with average rate found in part(a).

**skeeter** · May 25th 2009, 06:21 AM

Originally Posted by lisa1984wilson

I need help with this..I have 50 of these problems so if you can show me how to calculate this one I can do the rest myself...Thanks!
Let s(t)=√t
a.Find the average rate of change of s(t) with respect to t as t changes from t=1 to t=1/4
b.Use calculus to find the instantaneous rate of change of s(t) at t=1 and compare with average rate found in part(a).

average rate of change ...

$\frac{s(1) - s\left(\frac{1}{4}\right)}{1 - \frac{1}{4}}$

$\frac{1 - \frac{1}{2}}{1 - \frac{1}{4}} = \frac{2}{3}$

instantaneous rate of change at t = 1 ...

$\lim_{t \to 1} \frac{s(t) - s(1)}{t - 1}$

$\lim_{t \to 1} \frac{\sqrt{t} - 1}{t - 1}$

$\lim_{t \to 1} \frac{\sqrt{t} - 1}{(\sqrt{t} - 1)(\sqrt{t} + 1)}$

$\lim_{t \to 1} \frac{1}{\sqrt{t} + 1} = \frac{1}{2}$

Thread: Rate of Change

LinkBack

Thread Tools

Display

Rate of Change

Similar Math Help Forum Discussions

Relationship rate of change of diagonal and rate of change of area of rectangle

rate change

rate of change

rate of change

Rate of change

Search Tags