I don't know how to approach this question (help would be greatly appreciated!)
Find the average rate of change of the area of the circle with respect to its radius r as r changes from:
(i) 2 to 3, (ii) 2 to 2.5, (iii) 2 to 2.1

- anonymous

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- katieb

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- anonymous

Oh actually I think I got it... I differentiate pi*r^2 and then plug in the two values given and then find the average , right?

- freckles

\[\frac{\pi \cdot r_1^2 -\pi \cdot r_2^2}{r_1-r_2} \\ \pi \frac{r_1^2-r_2^2}{r_1-r_2} \\ \pi \frac{(r_1-r_2)(r_1+r_2)}{r_1-r_2} \\ \pi (r_1+r_2)\]

- anonymous

2pi(2) + 2pi(3)
------------- is this right?
2

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## More answers

- anonymous

for part (i)

- freckles

\[\frac{\pi \cdot r_1^2 -\pi \cdot r_2^2}{r_1-r_2} \\ \pi \frac{r_1^2-r_2^2}{r_1-r_2} \\ \pi \frac{(r_1-r_2)(r_1+r_2)}{r_1-r_2} \\ \pi (r_1+r_2)\]
this is the average rate of change of the area with respect to radius

- freckles

all you have to do is add your r's
and then multiply the result by pi

- anonymous

Ahhh I see! That makes sense!

- freckles

like I started with the one formula
change of area
divided by
change or radi

- freckles

\[\text{ average rate iof change of area}=\frac{A(r_1)-A(r_2)}{r_1-r_2}\]

- freckles

but was able to simplify this to that really pretty formula

- anonymous

Right, and that gives us the avg rate of change of area

- anonymous

Oh that sure is a beautiful formula *_*

- freckles

right if you wanted instantaneous rate of change at some r
you would find the derivative then plug in that r

- anonymous

Ohhh true!!

- Sepeario

how do you type text like that in the formula thing?

- anonymous

@freckles thanks again!! :)

- anonymous

@Sepeario click on 'equation'

- Sepeario

yeah but it always italicises the text

- freckles

\[\frac{ \text{ kitty eats kitten food} }{\text{ how to do } 5+\frac{6}{7} \text{ in a fraction }}\]

- freckles

\frac{ \text{ kitty eats kitten food} }{\text{ how to do } 5+\frac{6}{7} \text{ in a fraction }}

- Sepeario

how do you write normal text like that inside the equation thing?

- anonymous

Ohh hmm I have no clue, @freckles should know :P

- freckles

:) yes lol
|dw:1433574618995:dw|
put around that
just wherever you want text do \text{ }

- anonymous

Oooooh how did you know that?? :O

- Sepeario

oh thanks so much

- freckles

just a little experience with LaTeX

- freckles

I had to look up some things and also there is a LaTeX group if you want to get really good at it

- anonymous

Awesomeness ;D

- anonymous

Oh is there?

- freckles

http://openstudy.com/study#/groups/LaTeX%20Practicing!%20%3A)
there are some tutorials you can find somewhere in these threads they have posted

- anonymous

Thats great!! Thanks for the link! It'll be useful! :D

- freckles

By the way I do not claim to be a genius at it

- freckles

I just know some basic things

- anonymous

It's still a lot more that I know :P

- anonymous

than*

- yrelhan4

The "beautiful formula" thing kinda made me laugh. :P
Nice explanation though. :)

- anonymous

Haha @yrelhan4 yeah same here xD and yes, @freckles explains perfectly!

- freckles

awww how kind

- anonymous

^_^ just being honest :D

- freckles

goodnight and thanks
good luck with calculus

- anonymous

@freckles G'night and thank YOU for helping me out so much! Thanks! :)

- freckles

It was no problem

- anonymous

:) Sleep well

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