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Let f(t) = ln(0.5t) on the interval [1,4], where f measures the rate at which water is changing (in acre-feet/month) in a storage reservoir and t measures time in months. A positive value for f indicates that the reservoir is being replenished, so water levels are increasing. The graph below is of f(t) with 4 approximating rectangles.

Let f(t) = ln(0.5t) on the interval [1,4], where f measures the rate at which water is changing (in acre-feet/month) in a storage reservoir and t measures time in months. A positive value for f indicates that the reservoir is being replenished, so water levels are increasing. The graph below is of f(t) with 4 approximating rectangles.

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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Let f(t) = ln(0.5t) on the interval [1,4], where ƒ measures the rate at which water is changing (in acre-feet/month) in a storage reservoir and t measures time in months. A positive value for f indicates that the reservoir is being replenished, so water levels are increasing. The graph below is of f(t) with 4 approximating rectangles. 0 -1-
Transcribed Image Text:Let f(t) = ln(0.5t) on the interval [1,4], where ƒ measures the rate at which water is changing (in acre-feet/month) in a storage reservoir and t measures time in months. A positive value for f indicates that the reservoir is being replenished, so water levels are increasing. The graph below is of f(t) with 4 approximating rectangles. 0 -1-
(a) What are the units on the estimate provided by the approximation? (b) Is this sum a left-endpoint approximation or right-endpoint approximation and how do you know? (c) For the sum pictured: i. n = ii. a = iii. b = iv. Δt = v. to = vi. t₁ = (d) Explain what happens as n → ∞o? vii. t₂ = viii. t3 = ix. t₁ =
Transcribed Image Text:(a) What are the units on the estimate provided by the approximation? (b) Is this sum a left-endpoint approximation or right-endpoint approximation and how do you know? (c) For the sum pictured: i. n = ii. a = iii. b = iv. Δt = v. to = vi. t₁ = (d) Explain what happens as n → ∞o? vii. t₂ = viii. t3 = ix. t₁ =
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