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140Bquiz5csols

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

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1 MATH 140B QUIZ#5 Solutions Due: Tues Oct 2, 2007 Print Name: Instruction: For each of the functions y = f ( x ), compute y but DO NOT SIMPLIFY. 1. a) If y = cos 3 (2 x ) then y = 3 cos 2 (2 x ) · ( - sin(2 x )) · 2 b) If y = sin x x then y = x cos x - sin x · (1) x 2 c) If y = tan 2 x + tan( x 2 ) then y = 2 tan x · sec 2 x + sec 2 ( x 2 ) · 2 x d) If y = radicalbig x - x = ( x - x 1 2 ) 1 2 then y = 1 2 ( x - x 1 2 ) 1 2 · (1 - 1 2 x 1 2 ) . e) If y = 2 x 5 + x 3 x + 1 = 2 x 5 + x 3 ( x + 1) 1 2 , y = ( x + 1) 1 2 · (10 x 4 + 3 x 2 ) - (2 x 5 + x 3 ) · 1 2 ( x + 1) 1 2 (1) ( x + 1) . f) If y = x cot( x ) then y = x · bracketleftBig - csc 2 ( x ) · 1 2 x 1 2 bracketrightBig + (1) · cot( x ) . g) If y = sec parenleftbigg 1 x parenrightbigg then y = sec parenleftbigg 1 x parenrightbigg tan parenleftbigg 1 x parenrightbigg · ( - x 2 ) h) If y = 2 + cos 2 t then y = 1 2 (2 + cos 2 t ) 1 2 · 2 cos t · ( - sin t ) 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
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