Section 3.11 1. Find a linearization off(x) = Vx at suitably chosen integer near a = 26, at which the given function and its derivative are easy to find. %3D Use your linearization to estimate the value of V26. 2. Write a differential formula that estimates the change in diameter D of a tree if the circumference increases from Co to Co + dC. Recall that C = tD, so you can start by solving for D. Suppose that the diameter D of a certain tree is 12 inches one year. During the following year, the circumference increased by 1.5 inches. By about how much did the diameter increase that year? Write a differential formula that estimates the change in cross-sectional area A = ar² of a tree if the radius increases from ro to ro + dr. By about how much did the cross-sectional area of the tree above increase the year in question? (Recall that D = 2r.)

Section 3.11 1. Find a linearization off(x) = Vx at suitably chosen integer near a = 26, at which the given function and its derivative are easy to find. %3D Use your linearization to estimate the value of V26. 2. Write a differential formula that estimates the change in diameter D of a tree if the circumference increases from Co to Co + dC. Recall that C = tD, so you can start by solving for D. Suppose that the diameter D of a certain tree is 12 inches one year. During the following year, the circumference increased by 1.5 inches. By about how much did the diameter increase that year? Write a differential formula that estimates the change in cross-sectional area A = ar² of a tree if the radius increases from ro to ro + dr. By about how much did the cross-sectional area of the tree above increase the year in question? (Recall that D = 2r.)

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Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.7: Applications

Problem 14EQ

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