Question

Suppose that the amount of air in a balloon after t hours is given by V(t)=t3 -6t2 +35
Estimate the instantaneous rate of change of the volume after 5 hours.
Solution Find the ARC first:
A.R.C.=V(t)-V(5)/ t-5, so t^3 -6t^2 +35-10/ t-5, so, t^3-6t^2+25

How did he get 10?

Answer 1

I cant attach a file instead

Answer 2

hope that makes it easier to read

Answer 3

\[\lim_{t \rightarrow 5}\frac{V(t)-V(5)}{t-5}\]
\[=\lim_{t \rightarrow 5}\frac{(t^3-6t^2+35)-(5^3-6(5)^2+35)}{t-5}\]
Now you have like terms on top
simplify that for me and i will be back

Answer 4

ok that works

Answer 5

thanks

Answer 6

oh you just didn't understand how to plug in?

Answer 7

yeah pretty much; got confused from another exxample

Answer 8

thanks :$

Answer 9

ok and you are gonna want to approximate the instantaneous rate of change (above if you know limits you can find it exactly)
So just take values really close to 5 for t to find an approximation of the i.r.c.

Answer 10

yup learning limits atm