Math121SampleQuiz4Sols

Math121SampleQuiz4Sols - QUIZ #4 (SAMPLE SOLUTIONS) USE A...

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QUIZ #4 (SAMPLE SOLUTIONS) USE A SCIENTIFIC CALCULATOR! 1) Find the derivatives. Simplify where possible. (19 points total) a) Dx x ln 3 4 5 + () È Î Í ˘ ˚ ˙ (7 points) Method 1 =+ [] =◊ + ◊+ = + = x x x x 45 4 1 5 5 3 3 3 3 2 ln (Using Power Rule for Logs) 67 48 4 12 5 2 3 x x Method 2 = + = + ( ) = + + = + 1 5 5 1 5 3 12 5 5 3 4 3 4 3 4 3 3 2 23 3 3 4 x x xx x x 12 5 2 3 x x b) De x 3 4 2 + (4 points) + + + ++ 34 42 2 eD x x x 38 1 o r 2 4 3 44 22 ex e x
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c) Dxe x x 26 () (6 points) = [] + [] () = + [ ] =+ Dx e x De xe x e x x x x xx 2 6 62 6 (Product Rule) 6 xe x e d) De x 8 (2 points) = 0 (Hey, we're differentiating a constant….) 2) If fx x x = ln , find ¢ fe . Do not approximate. (8 points) ¢ () = () + =[] [ ] + È Î Í ˘ ˚ ˙ ¢ = fx Dx x xD x x x e ln ln ln ln ln (Product Rule) 1 1 1 1 11 2 3) Find the integrals. Simplify wherever possible. (33 points total) a) 41 0 7 3 d x -+ Ú (6 points) = Ê Ë Á ˆ ¯ ˜ - Ê Ë Á ˆ ¯ ˜ ++ =- + + 4 4 10 2 7 42 xC xxx C 57 Note: You could have used "Integrating-at-Sight" for the first term. b) x x dx 4 4 3 + Ê Ë Á ˆ ¯ ˜ Ú (7 points) - Ê Ë Á ˆ ¯ ˜ + + - - - Ú d x C 14 4 54 3 3 3 3 / / / 4 5 5/4 3 xxC
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c) xd x + () Ú 3 2 (7 points) =+ + Ê
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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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Math121SampleQuiz4Sols - QUIZ #4 (SAMPLE SOLUTIONS) USE A...

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