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3 is the question to be answered please. Thank yo

3 is the question to be answered please. Thank yo

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 13EQ
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#3 is the question to be answered please. Thank you!
2. Solve the initial value problem. f'(x)= e²* – sin 4x; f(0)=2 3. An evergreen nursery usually sells a certain shrub after 6 years of growth and shaping. The growth rate during those 6 years is approximated by h'(t)=1.5t +5, where t is the time in years and h is the height in centimeters. The seedlings are 12 cm tall when planted (t = 0.) a) Find h(t), the height after t years b) How tall are the shrubs when they are sold? 4. Given f(x)= x' on [0,2]: Estimate the area under the curve with n = 4 subintervals of equal width and using: a) left endpoints, A L, b) right endpoints, A R, c) midpoints, A z M, Make a sketch for each estimate that shows the rectangles with all of the appropriate x-values labeled. Round answers to the nearest hundredth. 5. Oil is leaking from a ruptured tanker. The rate at which the oil is leaking (in gallons per minute) is measured every hour. Estimate the total amount of amount of oil that leaked from the tanker during that period, using n=7 subintervals and left endpoints for the rates. 4 5 6. Time (hours) Rate (gal/min) | 87 3 76 68 62 57 53 50 46
Transcribed Image Text:2. Solve the initial value problem. f'(x)= e²* – sin 4x; f(0)=2 3. An evergreen nursery usually sells a certain shrub after 6 years of growth and shaping. The growth rate during those 6 years is approximated by h'(t)=1.5t +5, where t is the time in years and h is the height in centimeters. The seedlings are 12 cm tall when planted (t = 0.) a) Find h(t), the height after t years b) How tall are the shrubs when they are sold? 4. Given f(x)= x' on [0,2]: Estimate the area under the curve with n = 4 subintervals of equal width and using: a) left endpoints, A L, b) right endpoints, A R, c) midpoints, A z M, Make a sketch for each estimate that shows the rectangles with all of the appropriate x-values labeled. Round answers to the nearest hundredth. 5. Oil is leaking from a ruptured tanker. The rate at which the oil is leaking (in gallons per minute) is measured every hour. Estimate the total amount of amount of oil that leaked from the tanker during that period, using n=7 subintervals and left endpoints for the rates. 4 5 6. Time (hours) Rate (gal/min) | 87 3 76 68 62 57 53 50 46
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