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Stewart_Calc_7ET ch14sec04
MULTIPLE CHOICE
1. Find the equation of the tangent plane to the given surface at the specified point.
a.
b.
c.
d.
e.
2. Find the differential of the function
a.
b.
c.
d.
3. Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm
high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal
in the sides is 0.01 cm thick. (rounded to the nearest hundredth.)
a.
8.34
b.
6.99
c.
6.91
d.
6.7
e.
4. A boundary stripe 2 in. wide is painted around a rectangle whose dimensions are 100 ft by
240 ft. Use differentials to approximate the number of square feet of paint in the stripe.
a.
113
b.
113.81
c.
113.23
d.
113.89
e.
113.33
NUMERIC RESPONSE
1. Find the equation of the tangent plane to the given surface at the specified point.
2. Find an equation of the tangent plane to the given surface at the specified point.
3. Use differentials to estimate the amount of tin in a closed tin can with diameter 8 cm and
height cm if the tin is 0.04 cm thick.
4. Find the linearization L(x, y) of the function at the given point.
Round the answers to the nearest hundredth.
5. Use the linearization L(x, y) of the function.
at to approximate .
6. Find the differential of the function.
7. The wind-chill index I is the perceived temperature when the actual temperature is T and the
wind speed is v so we can write . The following table of values is an excerpt from
a table compiled by the National Atmospheric and Oceanic Administration. Use the table to
find a linear approximation to the wind chill index function when T is near
and v is near 30 kmh.
10
20
30
40
50
20
18
17
14
13
12
16
15
12
10
7
8
12
8
6
2
2
8
5
1
8. If and changes from (2, 1) to find dz.
SHORT ANSWER
1. Let and suppose that changes from to
(a) Compute (b) Compute
2. Find the differential of the function
3. Find the differential of the function
