Math121Quiz4Sols

Math121Quiz4Sols - QUIZ #4 (SECTIONS 4.3, 4.4, 5.1, 5.2)...

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QUIZ #4 (SECTIONS 4.3, 4.4, 5.1, 5.2) SOLUTIONS MATH 121 – FALL 2003 – KUNIYUKI 105 POINTS TOTAL, BUT 100 POINTS = 100% 1) Find the derivatives. Simplify where possible. (21 points total) a) Dx x ln 2 3 4 + () È Î Í ˘ ˚ ˙ (4 points) = + ◊+ = + = + 1 23 1 8 4 4 4 3 x x x x 8 3 4 x x b) Dx x x 22 ln (8 points) Method 1 = [] + [] () È Î Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ = + =+ È Î Í ˘ ˚ ˙ x x D x xx x D x xx x x x 2 2 1 ln ln ln ln ln can use Power Rule (Product Rule) 123 2l n 2 2 Method 2 = + = + È Î Í ˘ ˚ ˙ È Î Í ˘ ˚ ˙ x x D x x x x x x 2 2 2 2 2 2 1 2 1 2 ln ln ln ln (Product Rule) n 2 2
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c) De w w /9 () (4 points) = Ê Ë Á ˆ ¯ ˜ = w w 1 9 1 9 1 9 e w d) x xx 5 2 3 - (5 points) =◊ - =- - - -- 53 2 32 eD x x x 52 3 o r 1 0 1 5 22 33 ex x e 2) Let fx x x = ln 3 . Simplify where possible: (13 points total) a) Find ¢ . ¢ () = -◊() ¢ = - = Ê Ë Á ˆ ¯ ˜ - = - = - = - xD x x D x x x x x x x x Lo D Hi Hi D Lo the square of what s below Quotient Rule 3 2 3 2 6 2 6 1 3 3 13 ln ln ln ln ln 1 3ln 4 x x or 1l n 3 4 - x x b) Find ¢ f 1 .
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This note was uploaded on 09/08/2011 for the course MATH 121 taught by Professor Staff during the Spring '11 term at Mesa CC.

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Math121Quiz4Sols - QUIZ #4 (SECTIONS 4.3, 4.4, 5.1, 5.2)...

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