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Practice for MAT 265 Test 2
1.
Find the equation of the tangent line to the curve
x
2
−
xy
y
2
=
7
at the point
−
1,2
.
2.
A balloon is rising vertically above a level, straight road at a constant rate of 1 ft/sec. Just
when the balloon is 65 ft above the ground, a bicycle moving at a constant rate of 17 ft/sec
passes under it. How fast is the distance between the bicycle and balloon increasing 3
seconds later?
3.
The diameter of a tree was 10 inches. During the following year, the circumference grew 2
inches. Use differentials to determine how much the tree's diameter and crosssection area
grew.
4.
Air is being pumped into a spherical balloon so its volume is increasing at a rate of
2500 ft
3
/
sec
.
How fast is its diameter increasing when the radius is
75ft
?
Round your
answer to 4 decimal places and include units.
Recall the volume of a sphere is
4
3
r
3.
5.
Use logarithmic differentiation to find the derivative of the following functions
a)
f
x
=
x
sin
x
b)
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 Fall '08
 LIN
 Calculus

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