Math 181  Test 2  November 11, 1991

NAME: (PRINT) SSN:

1. Find the length of the curve given by x = t^{3}, y = 3t^{2}, 0 ≤ t ≤ 1.

2. Sketch the graph of r = 3 sin 2θ and find the area of one leaf.

Math 181  Test 2  November 11, 1991

In questions 3 and 4 determine whether the series converges or diverges, giving reasons.

3. ∑_{n=1}^{∞} \frac{n + 1}{\sqrt{n^{5} + n^{3} − 1}}

4. ∑_{n=2}^{∞} \frac{1}{n log n}

Math 181  Test 2  November 11, 1991

5.Compute: ∫_{2}^{5} \sqrt{5 + 4x − x^{2}} dx

6. Determine all values of x for which the following series converges.

∑_{n=1}^{∞} \frac{(−1)^{n}(x + 2)^{n−1}}{2n − 1}