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

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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

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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?
\[\frac{\pi \cdot r_1^2 -\pi \cdot r_2^2}{r_1-r_2} \\ \pi \frac{r_1^2-r_2^2}{r_1-r_2} \\ \pi \frac{(r_1-r_2)(r_1+r_2)}{r_1-r_2} \\ \pi (r_1+r_2)\]
2pi(2) + 2pi(3) ------------- is this right? 2

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for part (i)
\[\frac{\pi \cdot r_1^2 -\pi \cdot r_2^2}{r_1-r_2} \\ \pi \frac{r_1^2-r_2^2}{r_1-r_2} \\ \pi \frac{(r_1-r_2)(r_1+r_2)}{r_1-r_2} \\ \pi (r_1+r_2)\] this is the average rate of change of the area with respect to radius
all you have to do is add your r's and then multiply the result by pi
Ahhh I see! That makes sense!
like I started with the one formula change of area divided by change or radi
\[\text{ average rate iof change of area}=\frac{A(r_1)-A(r_2)}{r_1-r_2}\]
but was able to simplify this to that really pretty formula
Right, and that gives us the avg rate of change of area
Oh that sure is a beautiful formula *_*
right if you wanted instantaneous rate of change at some r you would find the derivative then plug in that r
Ohhh true!!
how do you type text like that in the formula thing?
@freckles thanks again!! :)
@Sepeario click on 'equation'
yeah but it always italicises the text
\[\frac{ \text{ kitty eats kitten food} }{\text{ how to do } 5+\frac{6}{7} \text{ in a fraction }}\]
\frac{ \text{ kitty eats kitten food} }{\text{ how to do } 5+\frac{6}{7} \text{ in a fraction }}
how do you write normal text like that inside the equation thing?
Ohh hmm I have no clue, @freckles should know :P
:) yes lol |dw:1433574618995:dw| put around that just wherever you want text do \text{ }
Oooooh how did you know that?? :O
oh thanks so much
just a little experience with LaTeX
I had to look up some things and also there is a LaTeX group if you want to get really good at it
Awesomeness ;D
Oh is there?
http://openstudy.com/study#/groups/LaTeX%20Practicing!%20%3A) there are some tutorials you can find somewhere in these threads they have posted
Thats great!! Thanks for the link! It'll be useful! :D
By the way I do not claim to be a genius at it
I just know some basic things
It's still a lot more that I know :P
than*
The "beautiful formula" thing kinda made me laugh. :P Nice explanation though. :)
Haha @yrelhan4 yeah same here xD and yes, @freckles explains perfectly!
awww how kind
^_^ just being honest :D
goodnight and thanks good luck with calculus
@freckles G'night and thank YOU for helping me out so much! Thanks! :)
It was no problem
:) Sleep well

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