# various calculus problem set

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1. Write the first five terms of the arithmetic sequence: a1 = 3; d = 3

2. A spinner is used for which it is equally probable that the pointer will land on any one of six regions. Three of the regions are colored red, two are colored green, and one is colored yellow. If the pointer is spun twice, find the probability it will land on green and then yellow.

3. Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limit properties can be applied:

4. A piecewise function is given. Use the function to find the indicated limits, or state that a limit does not exist.

5. A restaurant offers a choice of 5 salads, 9 main courses, and 3 desserts. How many possible 3-course meals are there?

6. Evaluate the given binomial coefficient:

7. Use the graph of f to find the indicated limit

8. Evaluate the given binomial coefficient:

9. How many 2-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0? No digit can be used more than once.

10. Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limit properties can be applied.

11. Use the empirical probability formula to solve the exercise. Express the answer as a fraction. Then express the probability as a decimal, rounded to the nearest thousandth, if necessary.

12. If the given sequence is a geometric sequence, find the common ratio: 4, 12, 36, 108, 324

13. Evaluate the factorial expression:

14. You are dealt one card from a standard 52-card deck. Find the probability that you are not dealt a 10.

15. Find the slope of the tangent line to the graph of f at the given point:

16. Find the derivative of f at x. That is, find f'(x).

17. The function f(x) = x3describes the volume of a cube, f(x), in cubic inches, whose length, width, and height each measure x inches. If x is changing, find the average rate of change of the volume with respect to x as x changes from 4 inches to 4.1 inches.

18. Evaluate the given binomial coefficient:

19. Use the formula for the value of an annuity to solve the problem. Round your answer to the nearest dollar.

Looking ahead to retirement, you sign up for automatic savings in a fixed-income 401K plan that pays 6% per year compounded annually. You plan to invest $3500 at the end of each year for the next 20 years. How much will your account have in it at the end of 20 years?

20. Write a formula for the general term (the nth term) of the arithmetic sequence. Do not use a recursion formula. Then use the formula for an to find the indicated term of the sequence.

21. Complete the table for the function and find the indicated limit:

22. Write the first five terms of the sequence whose general term is given:

23. Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r.

24. Use the Binomial Theorem to expand the expression and express the result in simplified form.

25. An explosion causes debris to rise vertically with an initial velocity of 9 feet per second. The functions (t) = -16t2 + 144t describes the height of the debris above the ground, s(t), in feet, t seconds after the explosion. What is the instantaneous velocity of the debris 5 second(s) after the explosion?

#### Solution Summary

The solution is comprised of detailed explanations of this set of problems covering all aspects of calculus and probability, such as limit, derivative, tangent line, binomial coefficient, geometric sequence and arithmetic sequence.