Unformatted text preview: Math 137 ASSIGNMENT 6 Fall 2006 Submit all boxed problems and all extra problems by 8:20 am. November 3.
All solutions must be clearly stated and fully justified. TEXT: Section 3.1 ~~ 55, (Read about left and right—hand derivatives in #46 on text page 175.) Section 3.6 1 43, I, 45, l I, 65, I, 69.
Section 3.10 — , 33. 37.
Section 3.11 ~ 3, I, 7. 9, , 13, , 33, 37, (Use Maple for the graphs), , 50. Page 181 , 12.
Pages 276—277 ~ [E], 21, EXTRA.PROBLEMS:
E6.1 Show that the iiinction f(a:) = —  111117 on :r > O has a negative derivative for all :5 > (1, and
1. hence has an inverse. f“. Find if"1 (1) and j'—1’(1). 1336.2 Use the deﬁnition of f’(a) to determine whether the function f(:L') : :U  1' — 1. I is (ilifferentiable
at :c = 1. Sketch a graph of f and 01‘ f’. E63 Find £0(:I:) (the linear approximation near a: = O) for /(I) = (1 + m)_1. The use this result to
1 1+ﬂ
graph of y = 9(1) and y = 1 — [2, showing the error in this approximation at f = 1. Show that the function 9U) = is approximately 1  1‘2 near t = 0. Sketch a qualitative N.B. Reference the derivative rules DSR, DPR. DQR, DCR. whenever used. (Abbreviations are
analogous to those for limits and continuity.) ...
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