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exam3-practice-solutions

# exam3-practice-solutions - \u ~ NAME g0 043 MATH 2200 Fall...

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Unformatted text preview: \u ~ NAME: g0 043 MATH 2200, Fall 2009 Practice Exam 3 Please hand only only clearly written work, not scratch paper. Clearly mark your ﬁnal an- swers for each problem. Partial credit will only be given on problems for which your work is clearly shown. The only allowable materials for this exam are paper, pens and pencils. No notes, textbooks or calculators will be allowed. (1) Suppose that :v and y satisfy the equation: my = 1n(:1:) Find the slope of the tangent line to the graph of this equation at the point (e, 0). [Hint : the change of base formula for exponential functions is: as 2 es 1“(‘1)] (2) Suppose that :1: and y are functions of t which satisfy the equation: 21‘ sin(y) + cos(:1:2) = 0 Find an equation for 211% in terms of a: and y assuming that \$5 = 1 (3) A balloon is expanding so that its volume is increasing at a constant rate 3 cm3 / sec. Using the fact that the volume is given by (4) Suppose that the price (P) and the demand (3:) for a commodity are related by the equation 2P2x +1n(P + :13) + % = 200 (a) Find % as a function of x and P. (b) Find 3—; as a function of m and P. (M l— l 2—?— :CA/9 (MYW‘ydl M \L/ (4) Suppose that the price (P) and the demand (as) for a commodity are related by the equation 1 2P2\$ + 1n(P + x) + F = 200 (a) Find % as a function of x and P. LYY‘QAA‘O.” \“XA (b) Find (‘11—; as a function of cc and P. Prx (>7. .— w (WHLA Ar , \ /~ 9 ”“3 (50\$ (~2PE ‘ P1—x (5) Suppose f(:1:) = 6"” + sin :10. Find f”’(a:). ' VGQWfXA {—A + c0\$>< a; (6) Suppose f(:c) = lnzr. Find f”’(x). )zl“ ’(m 75-x I AQHCQ :64) X—l-\: ’)<, “(A : —- ('3 >52" 'K +COSX -K ' :6 ——\$\’\)4 ,2 -3 f; 5 2X 5 x3 (7) Calculate the following indeﬁnite integral: / (ex + 2x2 — sin x) dm (8) Calculate the following indeﬁnite integral: 3 / x262” d3: (4:ng aluwészX E’Lﬂ. ': )QZA)‘ (9) Calculate the following indeﬁnite integral: ‘4 2" lYW‘ 'L = 0\ : l- 1‘ Old : L— AV g M W Z (A C‘ r 'L __ l. lax "’ C ,. H x J/ (10) Calculate the following indeﬁnite integral: (662 e2 + 3:) d1: X: 6 :+><>Ax 1V8 e ugliwfxal” (11) Calculate the following indeﬁnite integral: /x+5d\$ x (12) Calculate the following indeﬁnite integral: (13) Consider the following graph of a function f (at): In the spaces below, write either a ”+ or a —’ to describe the intervals on which the ﬁrst and second derivatives of f ( ) are positive or negative. ...
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