# Question about Limits and Derivatives

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Please show me all of your work so that I can understand how to do the problems correctly. Please double check all of your answers to that you are sure everything is correct. Thanks.

1. Find the limit L. Then use the definition to prove that the limit is L. .

2. Find the limit: .

3. Calculate the derivative of . Use trigonometric identities located in the back cover of the textbook to simplify.

4. Find the slope of the curve at the point ( ,1).

5. Evaluate the integral: .

6. Describe or sketch (if possible) the graph of the function . You must use the first and second derivative tests and name any intercepts, asymptotes, relative extrema, and points of inflection. Also include any intervals on which the function is increasing or decreasing, any types of concavity, or symmetry.

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##### Solution Summary

These questions show limits, derivatives, and points of inflection. The expert finds the slope of a curve at a point.

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Please show me all of your work so that I can understand how to do the problems correctly. Please double check all of your answers to that you are sure everything is correct. Thanks.

1. Find the limit L. Then use the definition to prove that the limit is L. .

Proof. For any , there exists such that for every , we have

ie.,

So,

2. Find the ...

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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