quiz7Asol - Solutions to Quiz 4B...

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Unformatted text preview: Solutions to Quiz 4B www.math.ufl.edu/˜harringt March 6, 2008 1. A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1 ft/s, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 ft from the wall? First, we must draw a picture of the situation and label what we know. S S x S10 S S S y We are give that dy = 1 and by using the Pythagorean Theorem, we see that dt x2 + y 2 = 102 . So when x = 6 we have that 62 + y 2 = 102 ⇒ y 2 = 100 − 36 = 64 ⇒ y = 8. d d2 (x + y 2 ) = (102 ) dt dt dx dy 2x + 2y =0 dt dt x dx dy =− dt y dt Thus, after substitution we have the following: dy x dx 6 3 =− = − ∗ 1 = − ft/s dt y dt 8 4 2. Let f and g be differentiable for the following questions. Circle True or False: (a) TRUE or FALSE: FALSE Should be d [f (x)g (x)] = dx d [f (x)g (x)] = dx d 1 (ln 10) = 10 dx f (x)g (x) f (x)g (x) + f (x)g (x) (Product Rule) (b) TRUE or FALSE: d FALSE dx (ln 10) = 0 (ln 10 is a constant) d (c) TRUE or FALSE: dx f (g (x)) = f (g (x))g (x) TRUE (Chain Rule) (d) TRUE or FALSE: TRUE d dx tan(x) = sec2 (x) 1 ...
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This note was uploaded on 07/10/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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