Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
Transcribed Image Text:11-15. Given the following:
Z1 = 4 – 3i
22
CALCULUS 3
MULTIPLE CHOICE
= 2+2i
11. Z, + Z2 is equal to
Choose the best answer. Write the letter of your choice on your answer sheet.
1. Which of the following functions will have the same differential equation as y=10?
С. у 3D 10х
d. y = 5
а. у
10x + 5
а. 8 — 6і
b. 8 + 6i
с. 6 — і
d. 6+ i
b. x = 10
12. Z, – Z2 is equal to
b. 2 + 5i
2. The general solution to dy – (3x2 – 3) dx = 0 is
a. y = x3 + 3x + c
b. y = x3 – 3x + c
3. Using the general solution of dy - (3x2 - 3) dx
be equal to
а. 2 — 5i
с. 8 — бі
d. 5 – 2i
с. у %3D х3 + 3x2 + с
d. y = x³ – 3x² + c
13. The product Z,Z2 is equal to
a. 14 – 2i
b. 2 + 2i
с. 2 — 2i
d. 14 + 2i
0, when x =
1 and y = 2, c will
14. The quotient of Z1 Z2 would be
b. =
%3D
1
а.
4
d.+i
7
7
+-i
4
1
7
c. 2 + 7i
С. 4
= 0 will be
а.
2
b. 3
d. 5
4
4
4
15. (Z1)2 is equal to
4. A particular solution to dy – (3x2 – 3) dx
а. у %3D х — 3х + 2
b. у 3D х3 — 3х + 4
5. The integrating factor of y' – 6y = 0 is
a. 25 – 24i
b. 7 – 24i
c. 24 – 7i
d. 7+ 24i
с. у %3D х3 — Зх— 2
d. y = x³ – 3x + 4
3
-
|
16-23. Consider the following auxiliary equations
m2 + 36 = 0
I.
a. e*
С. е бх
II.
m2 – 36 = 0
b. e-6x
d. e-*
III.
m2 – 6m + 9 = 0
6. The integrating factor of y' +
= 0 is
m2 – 6m + 10 = 0
т? — т — 6 3D 0
IV.
а. х
c. In x
V.
b. x2
d. 2
16. Which equation/s will have distinct real roots?
7. What can be said about y cos x dx + sin x dy = 0?
a. It is separable
b. It is exact
8. The differential equation y cos x dx + sin x dy = 0 can be written as
a. d(y cos x) = 0
b. d(y sin x) = 0
b. Il only
c. Il and V only
d. Il only
a. T only
17. Which equation/s will have repeated real roots?
c. It has an integrating factor
d. All of these
b. Il only
a. T only
18. Which equation/s will have pure imaginary roots?
c. II only
d. I and IV
%3D
c. d(x sin y)
b. Il only
d. IV only
a. Ionly
19. Which equation will yield a general solution of y = c1 sinh 6x + c2 cosh 6x
d. d(x cos y)
c. III only
9. What must be multiplied to both sides of the equation x*y? d(xy) + xy d
(2) =
b. Il only
d. IV only
c. II only
20. Which equation will yield a general solution of y = c1 sin 6x + C2 cos 6x
a. Tonly
to make the equation integrable?
b.
-2
с. у?
1
d.
x³y
d. IV only
a. x?
b. Il only
c. III only
a. Ionly
21. The general solution to m2 – 6m + 9 = 0 would be
a. y = c1 + c2e-3*
b. y = ce3x + Cze3x
C. y = C1e
d. y = c + cze3x
10. i? is equal to
а. -1
b. i
C.-i
d. 1
-3x
+ C2xe-3x
Transcribed Image Text:22. The general solution to m²
6m + 10 = 0 would be
-3x
-3x
sin x + C2e
a. y = C1e
b. y = ce3x sin x + cze3*
c. y = ce3* sin 10x + c2e3* cos 10x
d. y = ce3* sinh x + cze3x cosh x
COS X
COS X
29. What is L {cos?t} + L {sin?t} ?
s+1
1
С.
а.
s2+1
s2 +1
b.
s4+1
d.
S
23. The general solution to m² – m – 6 = 0 would be
a. y = c1es* + c2e
b. y = ce
c. y = c1e3* + cze2x
d. y = ce-3x + cze-2x
- 2x
-3x
+ cze2x
30. If cos?t =+cos 2t, what is L+ cos 2t}?
1
= -
2
1
1
CoS
1
1
S
+
s2+4
1
С.
2s
а.
2s
s2+4
1
b.
2s
1
24. The auxiliary roots of the differential equation (D4 + 2D² + 1)y = 0 are
b. 1, 1, -1, -1
2s2 +8
2s
2s2+8
а. 1, 1, 1, 1
c.i, i, -i, -i
d. 1, -1, i, -i
25. The general solution to (D4 + 2D2 + 1)y = 0 is
a. y = c1e* + c2xe* + c3x²e* + C4x³e*
b. y = c1 sinh x + c2 cosh x + C3 x sinh x + C4 x cosh x
C. y = c1 sin x + c2 cos x + C3 sinh x + C4 cosh x
d. y = c sin x + C2 cos x + C3 x sin x + C4 x cos x
26. L {e-t} is equal to
1
а.
С.
s+1
s+1
1
b.
S-1
S
d.
s-1
27. L {sinh -t + cosh t} is equal
2
1
4
С.
4s+1
а.
1
s+
4
4
S
b.
4s-1
d.
4
28. L {cosh?t – sinh?t} is equal to
1
1
С.
а.
s2-1
1
b.
s2+1
d. -
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