Fall 2009 Math 151
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Week in Review V
2.
ourtesy: David J. Manuel
3.
1.
Setion 3.3
(b)
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(d)
2.
4.
Find the veloity at time t.
What is the position and veloity
after 3 seonds?
When is the partile at rest?
Find the total distane traveled in
the rst 3 seonds.
5.
Same questions as above given s =
t
f (t) = 2
.
t +4
3.
A trash ompator is rushing a pile of
trash whih remains in the shape of a
ube.
(a)
(b)
2
1.
Find the average hange in the volume of the ube as the length of a
side hanges from 50 m to 40 m.
Find the rate of hange in the volume of the ube when the length
of a side is 50 m.
Setion 3.4
Compute the following limits:
(a)
(b)
sin x
Find the equation of the line tangent
to the graph of f (x) = x2 tan x at the
π
point where x = .
4
A partile moves in a line aording to
the funtion s = f (t) = t3 +3t2 −9t+5,
where t is in seonds and s is in feet.
(a)
Find and simplify the derivatives of
1 − cos x
f (x) =
and g(x) =
sin x
.
1 + cos x
(overing 3.3, 3.4)
1
cos x − 1
x→0
x2
lim
2x
x→0 sin 5x
tan 7x
lim
x→0 sin 3x
lim
1
Find all values of a suh that 0 ≤
a ≤ 2π and the line tangent to f (x) =
sin2 x + cos x at x = a is horizontal.
Given the identity sin 2x
=
2 sin x cos x, dierentiate the righthand side to obtain the derivative of
sin 2x.