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Problem: 1. Let I, = S1(1 - x²)" cos()dr, n = 0,1, 2, ... Show that 0 < In < 2 for all n.

Problem: 1. Let I, = S1(1 - x²)" cos()dr, n = 0,1, 2, ... Show that 0 < In < 2 for all n.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Problem: 1. Let In = S1(1 – x²)" cos()dx, n = 0,1, 2, .... Show that 0 < In < 2 for all n. 2. Show that the integral In satisfies the following reduction for- mula T°I, = 8n(2n – 1)In-1 – 16n(n – 1)I,-2 for n > 2. 3. For n = 0, 1, 2, . .., show that there exist integers a1, a1, a2, . . . , an such that 2n+1 - In = n! = ao + a17 + a2n² + • · . + an™". (Hint: Using Problem 2.) 4. Using Problems 1 and 3, show that a is irrational.
Transcribed Image Text:Problem: 1. Let In = S1(1 – x²)" cos()dx, n = 0,1, 2, .... Show that 0 < In < 2 for all n. 2. Show that the integral In satisfies the following reduction for- mula T°I, = 8n(2n – 1)In-1 – 16n(n – 1)I,-2 for n > 2. 3. For n = 0, 1, 2, . .., show that there exist integers a1, a1, a2, . . . , an such that 2n+1 - In = n! = ao + a17 + a2n² + • · . + an™". (Hint: Using Problem 2.) 4. Using Problems 1 and 3, show that a is irrational.
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