Practice Exam 1

# Practice Exam 1 - equal intervals. Arrange the numbers I ,...

This preview shows pages 1–4. Sign up to view the full content.

Mathematics 115b Mid-term # 1 2/19/08 Name: Section: Please answer all SIX questions; each question is worth TEN points. You may use the table of integrals supplied with the test. However, books, notes, calculators, computers, cellphones may NOT be used. 1 2 3 4 5 6 Total (1) Find the derivative of Z 2 x tan x t 2 + 1 dt

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
(2) Rotate the region bounded by x = y 2 and x = 1 about the line y = 3. Find the volume of the resulting solid. (3) Evaluate Z dx x 2 + 1 - x 2 - 3
(4) Let L 10 , R 10 , M 10 , T 10 be the approximations to the integral I = Z 2 1 1 /x dx given by the left and right endpoint rules, the midpoint rule and the trapezoidal rule, with 10

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: equal intervals. Arrange the numbers I , L 10 , R 10 , M 10 , T 10 in ascending order. [You don’t need to calculate numerical values, but a sketch may be helpful.] (5) Is the improper integral Z ∞ dx x 2 + 3 x + 2 convergent or divergent? You should give reasons, but you don’t have to evaluate the integral. (6) Calculate the integral Z ( π 2-1)-1 √ x + 1 sin √ x + 1 dx...
View Full Document

## This note was uploaded on 01/11/2010 for the course MATH 115 at Yale.

### Page1 / 4

Practice Exam 1 - equal intervals. Arrange the numbers I ,...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online