Determine whether the statement is true or false. If it is true, explainwhy. If it is false, explain why or give an example that disproves thestatement. If ∫a∞f(x) dx and ∫a∞ g(x) dx are both convergent, then ∫a∞ [f(x) + g(x)] dx is convergent.
Determine whether the statement is true or false. If it is true, explainwhy. If it is false, explain why or give an example that disproves thestatement. If ∫a∞f(x) dx and ∫a∞ g(x) dx are both convergent, then ∫a∞ [f(x) + g(x)] dx is convergent.
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 50E
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Determine whether the statement is true or false. If it is true, explain
why. If it is false, explain why or give an example that disproves the
statement.
If ∫a∞f(x) dx and ∫a∞ g(x) dx are both convergent, then ∫a∞ [f(x) + g(x)] dx is convergent.
Expert Solution
Step 1
Given: and are convergent.
To Show: is convergent.
We know, is convergent if .
Implies
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