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Consider the series. 8 an = Σ n=1 n=1 Let f(x) In (x) 5x² (Express numbers in exact form. Use symbolic notation and fractions where needed.) = In (n) 5n² . Find f'(x).

Consider the series. 8 an = Σ n=1 n=1 Let f(x) In (x) 5x² (Express numbers in exact form. Use symbolic notation and fractions where needed.) = In (n) 5n² . Find f'(x).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the series. Σ n=1 Let f(x) an = In (x) 5x² (Express numbers in exact form. Use symbolic notation and fractions where needed.) Incorrect ƒ'(x) = = 1,0⁰ ∞ Σ n=1 In (x) 5x² In (n) 5n² . ∞ Evaluate 6° (Express numbers in exact form. Use symbolic notation and fractions where needed.) Find f'(x). In (x) 5x² dx = dx. 10 (1+ln(2)) Identify the true statement(s) about the series and the integral. The Integral Test does not apply since f(x) is not continous on (1, ∞). f'(x) < 0 for all x ≥ 2, so ƒ is eventually decreasing. The integral ₂ f(x) dx is finite, so the series converges by the Integral Test. f(x) > 0 and is continuous for all x ≥ 2. The Integral Test does not apply since the function is only increasing when x ≥ 1. The integral ₂ f(x) dx is infinite, so the series diverges by the Integral Test.
Transcribed Image Text:Consider the series. Σ n=1 Let f(x) an = In (x) 5x² (Express numbers in exact form. Use symbolic notation and fractions where needed.) Incorrect ƒ'(x) = = 1,0⁰ ∞ Σ n=1 In (x) 5x² In (n) 5n² . ∞ Evaluate 6° (Express numbers in exact form. Use symbolic notation and fractions where needed.) Find f'(x). In (x) 5x² dx = dx. 10 (1+ln(2)) Identify the true statement(s) about the series and the integral. The Integral Test does not apply since f(x) is not continous on (1, ∞). f'(x) < 0 for all x ≥ 2, so ƒ is eventually decreasing. The integral ₂ f(x) dx is finite, so the series converges by the Integral Test. f(x) > 0 and is continuous for all x ≥ 2. The Integral Test does not apply since the function is only increasing when x ≥ 1. The integral ₂ f(x) dx is infinite, so the series diverges by the Integral Test.
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