Transcribed Image Text: 4. Find each differential.

a. du if u = x? – e*

b. dz if z = tcos(t), t = 0 and dt = .2

5. Our goal is to approximate In(.5), In(.8), and In(.9).

a. Letting f(x) = In(x), and by choosing a single appropriate value of a (for the purposes of

doing the above approximations), find the linear approximation to fat a:

b. Use the linear approximation to approximate the three values we seek.

c. Use the graph of f(x) = In(x) to explain how you know whether these are over-estimates

or under-estimates.

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d. Which of your approximations in part b would you expect to be best? Briefly explain

why.