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

• brandy
In summary, the person is asking for help with various topics in calculus, including squeeze theorem limits, constant coefficients, Fourier series, trigonometry substitutions for integration, integral and ratio tests, radius of convergence, and Taylor series. They also mention needing more practice with trigonometry substitutions and partial fraction decomposition. They are also looking for help with a few specific problems, including three trigonometry substitution problems and two integral test problems.
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)

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.

Last edited:

## 1. What topics will be covered on the test?

The test will cover a variety of things, including but not limited to: history, science, literature, math, and current events.

## 2. How many questions will be on the test?

The number of questions on the test will vary, but typically there will be around 50-100 questions.

## 3. Will the test be multiple choice or essay format?

The test will include a mix of both multiple choice and essay questions.

## 4. Are there any specific study materials or resources we should focus on?

The test will cover material from class lectures, readings, and discussions. It is important to review all of these materials in preparation for the test.

## 5. Will there be any extra credit opportunities on the test?

Extra credit opportunities will not be available on the test. However, if there is a bonus question, it will be indicated on the test and can provide some additional points.

• Calculus and Beyond Homework Help
Replies
2
Views
3K
• Calculus and Beyond Homework Help
Replies
6
Views
2K
• Calculus
Replies
13
Views
4K
• General Discussion
Replies
7
Views
10K
• General Math
Replies
2
Views
2K
• Differential Equations
Replies
10
Views
7K
Replies
6
Views
2K
• Chemistry
Replies
1
Views
2K
• Calculus
Replies
14
Views
3K
• STEM Career Guidance
Replies
2
Views
2K