Unformatted text preview: Math 137 ASSIGNMENT 7 Fall 2007 Submit all boxed problems and all extra problems by 8:20 awn, November 9.
All solutions must be. clearly stated and fully justiﬁed. Use the fOI'I‘Il'th given on UWACE
under Content. in the file Assignment Format for Math 135 and Math 137. TEXT PROBLEMS: Section 3.19 2, 3, I, 9, I, 13, IE, 17, I, 28, 33, 49, 41, 43 Section 41 14a), :50. I, 39, I, 41, I, Section 4.2 3, 5, 10, I, 19, 23, I. 28, Section 4.4 , E, 9, I, I, 19, I 21, I, I, I, 43, 55, I, 63. 69, I, I, 81 Section 4.8 ~ 1,  @‘ 34 EXTRA PROBLEMS: 137.] Using L’llR. or otherwise, evaluate each limit: ;_2_‘ 1 1 1':
“'3 1.3111001“ LEE—2% b) Egg—“37"”: C) ﬂightt1)!“ E72 At right is the graph of the (:lerivati've f’(:c) of
a certain function f(;7;) on the interval [(1, b]. ‘3 at) Explain how you know that “56) is non—
(leereasing on [(1. b]. 1)) Indicate any points where y 2 f(:L') has
a horizontal tangent. e) Explain what happens to the graph y 2 ﬁx) near the points you found in b). 0,. b
137.3 Find Gill!) (the linear up])i'oxiinution near :1, = (l) for [(33) = (l + :‘IZ’)_1. Then use. this
result to Show that the function g([.) = 1 + t3 is npproxnnutely l—t" near 1 = 0. Sketch a qualitative graph of y = g(i.) and y = 1—1.”, showing the error in this approximation
at i‘ = l. ...
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