Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Two bonus problems for math 141 students related to the convergence of integrals with non-positive roots polynomials. The first problem asks how to determine if the integral ∫f(x)g(x)dx converges or diverges when g(x) has no non-negative roots. The second problem extends the result to algebraic functions that are not rational. Students are encouraged to make an educated guess and prove their answer using the comparison theorem.
Typology: Assignments
1 / 1
This page cannot be seen from the preview
Don't miss anything!
Math 141 Homework # Due Tuesday 12/4/07 Bonus Problems
Bonus Problem #1 Suppose that you are given two polynomials f (x), g(x) such that g(x) has no non- negative roots. How can you tell whether
∫ (^) ∞
0
f (x) g(x)
dx
converges or diverges? (Hint: Make an educated guess, then prove it using the Comparison Theorem on p. 429.)
Bonus Problem #2 Generalize the result of the first problem to include functions that are algebraic but not rational (i.e., involve roots as well as polynomials; see p. 33).
