math final 2007 fall

A 4 4 fxh 2 h 000 200 x4 lim f x 4 lim lim 7 x3 10 x3

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Unformatted text preview: ined at x 4 x 1 x1 x9 d 1 ln x5 1 dx 2 7 x 8 (the tangent line) y e5 x 1 7 x 4 3 1/ 2 7 2/3 ln x3 1 4 x3 2 7 x4 1 ln x 5 1 2 4 1 5x 2 x5 1 2 ln x3 1 1/ 3 e5 x 5 2 ln x3 1 2 2 3x x3 1 OR f d ln dx x f x x5 1 1/ 2 3 2 x 1 x3 1 x5 1 2 1/ 2 x3 1 x 5 x3 1 1 2 2 1/ 2 d dx 1 x5 1 2 x5 1 1/ 2 x3 1 1/ 2 2 5x4 x3 1 x5 1 2 2 1/ 2 2 x3 1 1 3x 2 (c) dy dx 6 ln y d x 2 tan x sin 2 x 7 cos 1 9 x dx dy x 2 sec2 x tan x 2 x cos 2 x 7 14 x 6 dx ln 4 x 1 1 dy y dx 2x ln y 4 4x 1 2x d ln y dx 2 x ln 4 x 1 dy dx ln 4 x 1 2 fx f0 dy 8. dx d dx 2x 7 2x 4 4x 1 42 x 3 3 2x 2x 1 2x 7 4 2x 7 2x 7 14 2 x 7 8x 4x 1 2x 2 ln 4 x 1 2e 2 x 4 e2x x 1 4 xe 2 x 4 6 7 2x 7 2 2x 3 4 2x 7 14 2x 7 14 2 x 8 8 2x 7 dy 3 0 (numerator = 0) 6x 2 x dx Therefore, the function has a horizontal tangent at x 0 and at x 2 . To...
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This note was uploaded on 11/23/2012 for the course BIOL 102 taught by Professor Josephdent during the Spring '12 term at McGill.

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