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Stewart_Calc_7ET ch03sec03
MULTIPLE CHOICE
1. Find the given derivative by finding the first few derivatives and observing the pattern that
occurs.
a.
b.
c.
d.
e.
None of these
2. If f is the focal length of a convex lens and an object is placed at a distance v from the lens,
then its image will be at a distance u from the lens, where f ,v ,and u are related by the lens
equation
.
Find the rate of change of v with respect to u.
a.
b.
c.
d.
e.
3. Find the derivative of the function.
= 3 sin x + 9x – 9
a.
3 sin x + 9
b.
3 cos x + 9
c.
–3 sin x + 9
d.
–3 cos x + 9
4. Find the derivative of the function.
a.
b.
c.
d.
5. A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its
equation of motion is , where t is in seconds and x in centimeters.
Find the velocity at time t.
a.
b.
c.
d.
e.
NUMERIC RESPONSE
1. Find an equation of the tangent line to the curve at the point .
2. Find the limit.
3. Differentiate.
4. Calculate .
5. Find the derivative of the function.
6. Differentiate.
SHORT ANSWER
1. Find the derivative of the function.
2. Find the derivative of the function.
3. A body moves along a coordinate line in such a way that its position function at any time t is
given by
where is measured in feet and t in seconds. Find the velocity and acceleration of the
body when .
4. A 20-ft ladder leaning against a wall begins to slide. How fast is the angle between the
ladder and the wall changing at the instant of time when the bottom of the ladder is 13 ft
from the wall and sliding away from the wall at the rate of 4 ft/sec? Round the answer to the
nearest hundredth.
(figure not to scale)
5. Find the derivative of the function.
20 ft
