For each of the following integrals predict whether the improper integral converges In this case...

90.2K

Verified Solution

Question

Basic Math

For each of the following integrals predict whether the improper integral converges In this case we re looking for a casual comparison that we would use to guide our search for a comparison integral that would prove convergence or divergence For example for 36 x 1 For convergence enter converges or diverges Si dx for large x the integrand looks like 1 x so we predict the integral diverges x 6 S8 da for larger the integrand looks like 8 8 for large x the integrand looks like for large x the integrand looks like S z7 dx 7 de 00 8 Six 1 e 6 1 8x 6 1 d for large x the integrand looks like 113 so we predict the integral converges so we predict the integral diverges so we predict the integral converges so we predict the integral diverges Hint Use the largest powers of x or e without coefficient in the numerator and denominator to determine your comparison

Answer & Explanation Solved by verified expert

Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:

Unlimited Question Access with detailed Answers
Zin AI - 3 Million Words
10 Dall-E 3 Images
20 Plot Generations
Conversation with Dialogue Memory
No Ads, Ever!
Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!

Become a Member

Transcribed Image Text

For each of the following integrals predict whether the improper integral converges In this case we re looking for a casual comparison that we would use to guide our search for a comparison integral that would prove convergence or divergence For example for 36 x 1 For convergence enter converges or diverges Si dx for large x the integrand looks like 1 x so we predict the integral diverges x 6 S8 da for larger the integrand looks like 8 8 for large x the integrand looks like for large x the integrand looks like S z7 dx 7 de 00 8 Six 1 e 6 1 8x 6 1 d for large x the integrand looks like 113 so we predict the integral converges so we predict the integral diverges so we predict the integral converges so we predict the integral diverges Hint Use the largest powers of x or e without coefficient in the numerator and denominator to determine your comparison