(e) Determine whether the integral answer. The integral f(2) = 2 1x-21 [f(r) dr is convergent, divergent or indeterminate. Justify your X [" dx is improper at x = 2 where the denominator is zero. Since [* f(x) dr = √ √x=2 - 2 = (x-2) 1/2 and the exponent 1/2 < 1, it follows that the integrals converges by the theorem on sufficient conditions for the convergence of improper integrals at a point. We may calculate it as X 2 2 x-2+2 dx = dx = 12 x-2 S 2 = 3 x- x-2 dx +4 4 +41 4 16√2 [(x − 2)³/2] + 4[√√x − 22 = 3 dx 2√√x-2

(e) Determine whether the integral answer. The integral f(2) = 2 1x-21 [f(r) dr is convergent, divergent or indeterminate. Justify your X [" dx is improper at x = 2 where the denominator is zero. Since [* f(x) dr = √ √x=2 - 2 = (x-2) 1/2 and the exponent 1/2 < 1, it follows that the integrals converges by the theorem on sufficient conditions for the convergence of improper integrals at a point. We may calculate it as X 2 2 x-2+2 dx = dx = 12 x-2 S 2 = 3 x- x-2 dx +4 4 +41 4 16√2 [(x − 2)³/2] + 4[√√x − 22 = 3 dx 2√√x-2

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

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