Questions and answers for a test covering a variety of things?

[brandy]

im trying to study but i have um misplaced my textbook. (it ran away from me, after i neglected it whilst doing other assesments)

so i would greatly appreciate just a couple questions with answers, (feel free to give me more though ;) )
on any of these things (in order of priority)

- squeeze theorem limits involving things that are not trigs
- constant coeficients (complex, resonance, and nonhomogeneous and all these i think i want some working done because I am not that good at these)
- Fourier series
- trigonometry substitutions for integration
- integral test (in a context or situation or something)
- ratio test (in a context or situation or something)
- radius of convergence (in a context or situation or something)
- taylor series (harder ones for someone who has just been introduced to them maybe)

 

[Char. Limit]

Let's see... a few trig sub problems first, I suppose. Try these:

$$\int x^2 \sqrt{9 - x^2} dx$$

$$\int \frac{1}{x \sqrt{x^2 - 1}}$$

$$\int \frac{1}{1 - x^4}$$

Hint: On the third problem, use partial fraction decomposition first.

And a couple of integral test problems... are the following series convergent?

$$\sum_{n=2}^\infty \frac{1}{n log_e(n)}$$

$$\sum_{n=1}^\infty \frac{n^3}{e^{n^2}}$$

And for what p is the following series convergent?

$$\sum_{n=1}^\infty \frac{1}{n^p}$$

I'll think of questions for the other areas soon.