140Bquiz5csols - 1 MATH 140B Print Name: QUIZ#5 Solutions...

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Unformatted text preview: 1 MATH 140B Print Name: QUIZ#5 Solutions Due: Tues Oct 2, 2007 Instruction: For each of the functions y = f (x), compute y but DO NOT SIMPLIFY. 1. a) If y = cos3 (2x) sin x x then y = 3 cos2 (2x) (- sin(2x)) 2 x cos x - sin x (1) x2 y = 2 tan x sec2 x + sec2 (x2 ) 2x then 1 1 1 1 1 y = (x - x 2 )- 2 (1 - 2 x- 2 ). 2 1 1 b) If y = then y = c) If y = tan2 x + tan(x2 ) then 1 1 d) If y = x- x = (x - x 2 ) 2 e) 2x5 + x3 2x5 + x3 = If y = 1 , x+1 (x + 1) 2 If y = x cot( x) 1 (x + 1) 2 (10x4 + 3x2 ) - (2x5 + x3 ) 2 (x + 1)- 2 (1) y = . (x + 1) f) then 1 1 y = x - csc2 ( x) 2 x- 2 + (1) cot( x). 1 tan x 1 x 1 g) If y = sec 1 x then y = sec (-x-2 ) h) If y = 2 + cos2 t then y = 1 (2 + cos2 t)- 2 2 cos t (- sin t) 2 For the last two questions, find the equation of the tangent line to the graph of the given function at the indicated point. Put your answer in the form y = mx + b. i) If y = y =3 2x + 3 x-1 2x + 3 x-1 3 at P (2, 343) 2 then 2x + 3 x-1 2 (x - 1)(2) - (2x + 3)(1) =3 (x - 1)2 -15(2x + 3)2 -5 = . (x - 1)2 (x - 1)4 Therefore, y (2) = -735 and we get (y - 343) = -735(x - 2) or y = -735x + 1813. j) If y = x sin 2x at P (, 0) then y = x cos(2x) 2 + 1 sin 2x. Therefore, y () = 2 and hence (y - 0) = 2(x - ), or y = 2x - 2 2 . ...
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This note was uploaded on 03/30/2008 for the course MATH 140B taught by Professor Fabbri,marc during the Fall '07 term at Pennsylvania State University, University Park.

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