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.
 Fall '08
 ALL
 Math, Calculus, Geometry

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