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Stewart_Calc_7ET final exam
1. The graphs of and are given. For what values of x is ?
a.
b.
c.
–4, 12
d.
0
e.
4, 2
2. If , evaluate the difference quotient .
a.
b.
c.
h
d.
e.
None of these
3. How would you define in order to make f continuous at ?
a.
b.
c.
d.
e.
None of these
4. If an equation of the tangent line to the curve at the point where
a.
b.
c.
d.
e.
None of these
5. The height (in meters) of a projectile shot vertically upward from a point m above
ground level with an initial velocity of 25.48 m/s is after t seconds.
a) When does the projectile reach its maximum height?
b) What is the maximum height?
a.
b.
c.
d.
e.
6. Use implicit differentiation to find an equation of the tangent line to the curve at the given
point.
a.
b.
c.
d.
e.
7. Find f.
a.
b.
c.
d.
e.
8. Find the number c that satisfies the conclusion of the Mean Value Theorem on the given
interval.
,
a.
b.
c.
d.
e.
None of these
9. A piece of wire m long is cut into two pieces. One piece is bent into a square and the
other is bent into an equilateral triangle. How should the wire be cut for the square so that
the total area enclosed is a minimum?
Round your answer to the nearest hundredth.
a.
m
b.
m
c.
m
d.
m
e.
m
10. Find the area of the region that lies under the given curve. Round the answer to three
decimal places.
a.
b.
c.
d.
e.
9
4
11. The acceleration function (in m / ) and the initial velocity are given for a particle moving
along a line. Find the velocity at time t and the distance traveled during the given time
interval.
a.
b.
c.
d.
e.
12. Find the average value of the function on the interval . Round your
answer to 3 decimal places.
a.
0.288
b.
6.228
c.
0.3
d.
e.
12
13. Find the volume of the solid obtained by rotating the region bounded by the given curves
about the specified axis.
a.
b.
c.
d.
e.
None of these
14. Evaluate the integral.
a.
b.
c.
d.
e.
15. Evaluate the integral.
a.
b.
c.
d.
e.
16. The masses are located at the point . Find the moments and and the center of
mass of the system.
;
a.
b.
c.
d.
e.
17. Find the length of the curve.
a.
25.05
b.
13.05
c.
36.05
d.
e.
None of these
18. Which equation does the function satisfy?
a.
b.
c.
d.
e.
19. Solve the initial-value problem.
a.
b.
c.
d.
e.
20. Set up an integral that represents the length of the curve. Then use your calculator to find the
length correct to four decimal places.
a.
b.
c.
d.
e.
21. Determine whether the series is convergent or divergent by expressing as a telescoping
sum. If it is convergent, find its sum.
.
a.
b.
diverges
c.
d.
e.
22. Find the sum of the series.
a.
b.
c.
d.
e.
23. Find a nonzero vector orthogonal to the plane through the points P, Q, and R.
a.
b.
c.
d.
e.
None of these
24. Find the curvature of .
a.
b.
c.
d.
e.
25. If , evaluate .
a.
b.
c.
d.
e.
26. Find for the function .
a.
b.
c.
d.
e.
27. Find the directional derivative of at the point (1, 3) in the direction
toward the point (3, 1).
a.
b.
c.
d.
e.
None of these
28. Use spherical coordinates.
Evaluate , where is the ball with center the origin and radius .
a.
b.
c.
d.
e.
None of these
29. Find the gradient vector field of f.
a.
b.
c.
d.
e.
None of these
30. Evaluate the line integral.
a.
b.
c.
d.
e.
NUMERIC RESPONSE
1. The graphs of and are given.
Find the values of and .
2. The top of a ladder slides down a vertical wall at a rate of 0.1m/s . At the moment when the
bottom of the ladder is 3 m from the wall, it slides away from the wall at a rate of 0.2 m/s .
How long is the ladder?
3. Find the local and absolute extreme values of the function on the given interval.
,
4. If , find the Riemann sum with n = 5 correct to 3 decimal places,
taking the sample points to be midpoints.
5. Evaluate the integral using the indicated trigonometric substitution.
6. Find the volume of the resulting solid if the region under the curve
from to is rotated about the x-axis. Round your answer to four decimal places.
7. Find the length of the curve.
,
8. Use Euler’s method with step size 0.1 to estimate , where is the solution of the
initial-value problem. Round your answer to four decimal places.
9. Solve the initial-value problem.
10. Find the area of the region that is bounded by the given curve and lies in the specified
sector.
11. Calculate the given quantities if
12. Find the unit tangent vector for the curve given by .
13. Find all the second partial derivatives of
14. Find the volume of the given solid.
Under the paraboloid and above the rectangle .
15. Use Lagrange multipliers to find the maximum and the minimum of f subject to the given
constraint(s).
16. Find the volume of the given solid.
Under the paraboloid and above the rectangle .
