Calculus II, Spring 2014

Quiz 1

Mar 06, 2014 Show all details.

1. Solve for x\frac{dy}{dx} + 2y = 1 − \frac{1}{x} on x > 0 with y(1) = \frac{1}{2}.

2. State (need not prove) the integral test for series with positive terms (a_{n} > 0). Then give an example of a series that can be found convergent using this test.

3. State (need not prove) the ratio test for series with positive terms (a_{n} > 0). Then give an example of a series that can be found convergent using this test.

4. State (need not prove) the root test for series with positive terms (a_{n} > 0). Then give an example of a series that can be found convergent using this test. The examples in the last 3 questions need not be different.

5. State (need not prove) the Leibniz’s Theorem for alternating series. Then give an

example of a conditionally convergent series. Note: do study the proof for the midterm.

Calculus II, Spring 2014

Quiz 1

Mar 06, 2014 Show all details.

1. Solve for x\frac{dy}{dx} + 2y = 1 − \frac{1}{x} on x > 0 with y(1) = \frac{1}{2}.

2. State (need not prove) the integral test for series with positive terms (a_{n} > 0). Then give an example of a series that can be found convergent using this test.

3. State (need not prove) the ratio test for series with positive terms (a_{n} > 0). Then give an example of a series that can be found convergent using this test.

4. State (need not prove) the root test for series with positive terms (a_{n} > 0). Then give an example of a series that can be found convergent using this test. The examples in the last 3 questions need not be different.

5. State (need not prove) the Leibniz’s Theorem for alternating series. Then give an

example of a conditionally convergent series. Note: do study the proof for the midterm.