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# mid2sol - 1 Solve the diﬁerential equation dy 2 csc 51...

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Unformatted text preview: 1. Solve the diﬁerential equation dy __ _ 2 csc( 51:) cot(2:1:) with initial condition y(%) = 1. awﬂﬂ J.— r. v a ~rC i 3 2. A 5~f00t tall woman is walking away from a 14-foot tall lamppost. When the tip of her shadow is moving at a rate of 3 ft / sec, how fast is the woman walking? \. 29.4.23 3. Find the value of a: at which the function ﬂit) = (9: - 3:?)1/‘3, where p > 1 and q > 1, attains its maximum on the interval [0, 1]. (You do not have to verify that it is the maximum.) 4. Let 23:2 — 1 [:4 )n 01:15] (a) Find the horizontal asymptotes of f(:€), if it has any. .— - (b) Find all the critical points of ﬁx). (You do not have to Ll 3 l7 0" ”if :1 determine the local maxima and minima.) _,... i a b” l (16L) {1:00 Xi“: £3, X-"i: J'a/K? 5. Prove that f(:L‘) x ﬁsts —:I:2 +a:- 10 is an increasing function for all cc. 79510:» atmzf/QJZ‘quwaﬁi-IDD Haax , _ 3 .. 01(x)-/C7c»2-0 ‘/ V34, Kgrl/f 22(6)) ’57» yin—24878 JE‘PO ‘°"“"’"““’" J 30;) wﬁf—Mﬁﬂ =7; A0 gaping/U ...
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