10 questions

20 minutes

See All test questions

Calculator Disallowed

1. Given the equation y = 3 sin^{2}, what is an equation of the tangent line to the graph at x = π?

2. Which of the following statements about the series is true?

3.

The graph of f for -1 ≤ x ≤ 3 consists of two semicircles, as shown above. What is the value of

4. The series expansion for is

5. If for all positive values of k, then which of the following could be the graph of f ?

6. Which of the following is the Taylor series for f (x) = x^{2} cos x about x = 0?

7.

The graph of the polar curve r = 3 - sin θ is shown above. Which of the following expressions gives the area of the region enclosed by the curve?

8. What are all values of x for which the series converges?

9.

The graph of f is shown above, and . Which of the following is a possible graph of g ?

10. The series satisfies the hypotheses of the alternating series test, i.e.,, and If S is the sum of the series and s_{n} is the nth partial sum, what is the minimum value of n for which the alternating series error bound guarantees that |S - s_{n} | < 0.1?