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q2 - Honors Calc 1 MAC3472 3203 Quiz Q2 Prof JLF King...

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Honors Calc 1 MAC3472 3203 Quiz Q2 Prof. JLF King 14Apr2008 Note. This is an open brain, open HHA, closed book, quiz. Please fill in the blanks. Show no work; no partial credit. Please be sure to write expressions unambigu- ously e.g, the expression “1 /a + b ” should be bracketed either [1 /a ] + b or 1 / [ a + b ]. Be careful with negative signs! Differentiation Facts. You may use that sin 0 = cos and cos 0 = sin. Also log 0 ( t ) = 1 /t . Q2a: z Prof. King believes that writing in complete, coherent sentences is crucial in communicating Mathemat- ics, improves posture, and whitens teeth. Circle one: True! Yes! What’s a sentence? a Define a product function g := sin · log. So g 0 ( t ) = ; b Recall that tan = sin / cos. Thus tan 0 ( θ ) = . c Let α ( x ) := e [2 x 7 + 7 x ] . Then α 0 ( x ) = . d Below, f and g are differentiable fncs with f (2) = 3 , f 0 (2) = 19 , f (3) = 5 , f 0 (3) = 17 , g (2) = 11 , g 0 (2) = 1 2 , g (3) = 13 , g 0 (3) = 7 , g (5) = 23 , g 0 (5) = 29 . Define the composition h := g f . Then h (2) = . . . . . . ; h 0 (2) = . . . . . . . . . . . . . . . . . . . . . . . . . . . Please write each answer as a product of numbers; do not multiply out.
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