{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Exam_exam_2_

# Exam_exam_2_ - f What kinds of local approximations to f...

This preview shows page 1. Sign up to view the full content.

MIDTERM 2 — MATH 141 — FALL 2002 — BOYLE Use exactly ONE answer sheet per question (use the back of the sheet if needed). Put your name, your TA’s name and the question number on EACH page. Put a BOX around the Fnal answer to a question. No books, no notes, no calculators. Before handing in your test: on your Frst answer sheet, please copy the pledge, and sign. ———————————————————————————————————– 1 . Compute the following integrals. ( a ) (20 points) Z 5 x ( x - 2)( x - 3) dx ( b ) (20 points) Z tan x cos 3 x dx 2 . (20 points) Compute the following integral. Z 1 w 2 + 2 w + 5 dx 3 (a) (20 points) Compute the following integral. Z x 5 ln( x ) dx (b) (5 points) The Trapezoidal Rule for approximating R b a f ( x ) dx is built out of locally linear approximations to the function
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: f . What kinds of local approximations to f are used to build up the Left Endpoint and Simpson’s Rules? (c) (5 points) Let S n denote the Simpson’s Rule estimate for a given R b a f ( x ) dx and let E n = | S n-R b a f ( x ) dx | . Suppose that the error estimate for Simpson’s Rule shows E 10 ≤ 1. How big should n be to guarantee E n ≤ . 000 000 01 ? 4 . (15 points) ±or each integral below, give the appropriate description: ∞ ;-∞ ; DNE (does not exist); or CONVERGES (i.e. the improper integral is well deFned and converges to a Fnite real number–you don’t have to compute it). No proof required. ( a ) Z 1 1 √ x dx ( b ) Z 2 1 ( x-1) 2 dx ( c ) Z ∞ 1 sin 2 ( e x ) x 2 dx...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online