Calculus Practice Final Help!

[shortyofhb]

- Find the area of the region that lies inside r=3cos(θ) and outside r=2

I tried solving it but go stuck when solving for θ and not getting a clean number.


- Find the power series representation for the function and determine the interval of convergent for f(x) = (x^2 - 1) / (x^2 + 4)

I have no idea what to do on this one.

Thank you for the help!

 

[Steven G]

Hi,
How can we help you when you did not show us your work? We need to be able to show you where you made a mistake and how to get back on the right path to your solution.

If you had read the forum's guidelines you would have received help by now since it states in part that you have to solve your own problems with our help. If you fail to show us your work we can not really help.

So please post back showing us you work. Thanks.

 

[HallsofIvy]

Have you actually done the indicated division?

Since both numerator and denominator are quadratic with leading coefficient 1 the first division is \(\displaystyle \frac{x^2}{x^2}= 1\). Then the "remainder" is \(\displaystyle x^2- 1- (x^2+ 4)= -5\). \(\displaystyle x^2\) goes into -5 \(\displaystyle -5x^{-2}\) times so now the quotient is \(\displaystyle 1- 5x^{-2}\) and the "remainder is \(\displaystyle -5+ 0x^{-2}- 5x^{-2}(x^2+ 4)= -5+ 0x^{-2}- 5- 20x^{-2}= 20x^{-2}\). Then \(\displaystyle x^2\) divides into \(\displaystyle 20x^{-2}\) \(\displaystyle 20x^{-4}\) times giving a quotient of \(\displaystyle 1- 5x^{-2}+ 20x^{-4}\).

Keep doing that until you can "guess" (and then prove) a general term.