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1. (a) Use the integral test to show that the series 1 = 1 + 2 1 Σ 3 n21 is divergent. As part of your answer, state the three conditions that a function f must satisfy before the integral test can be applied, and show that f(x) = 1/x does indeed satisfy these conditions.

1. (a) Use the integral test to show that the series 1 = 1 + 2 1 Σ 3 n21 is divergent. As part of your answer, state the three conditions that a function f must satisfy before the integral test can be applied, and show that f(x) = 1/x does indeed satisfy these conditions.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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1. (a) Use the integral test to show that the series 1 = 1 + 2 1 Σ 3 n>1 is divergent. As part of your answer, state the three conditions that a function f must satisfy before the integral test can be applied, and show that f(x) = 1/x does indeed satisfy these conditions. (b) Ugh is a Stone Age stone man. He is really good at making bricks. His intention is to make a bridge across a ravine by stacking bricks according to the picture below where the top brick has an overhang of 1/2, the second brick overhangs by 1/4, the third by 1/6, and so on with the n-th brick (on the bottom) having an overhang of 1/(2n). The total overhang is 1 + - + - + 4 1 +...+ 8 1 6. 2n Is there a maximum width ravine that can, in theory, be crossed in this manner? Explain.
Transcribed Image Text:1. (a) Use the integral test to show that the series 1 = 1 + 2 1 Σ 3 n>1 is divergent. As part of your answer, state the three conditions that a function f must satisfy before the integral test can be applied, and show that f(x) = 1/x does indeed satisfy these conditions. (b) Ugh is a Stone Age stone man. He is really good at making bricks. His intention is to make a bridge across a ravine by stacking bricks according to the picture below where the top brick has an overhang of 1/2, the second brick overhangs by 1/4, the third by 1/6, and so on with the n-th brick (on the bottom) having an overhang of 1/(2n). The total overhang is 1 + - + - + 4 1 +...+ 8 1 6. 2n Is there a maximum width ravine that can, in theory, be crossed in this manner? Explain.
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