# ENT 300 exam II

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1. Integral operator is a(n) _______ operator
area
2. Given: g(x) = intg{ f(x) dx }. The constant of integration is _____ g(x)
independent of
3. Given: g(x) = intg{ f(x) dx }. The first value of g(x) must include an external value (or number), which is called the constant of integration.
true
4. Given: g(x) = intg{ f(x) dx }. The first value of g(x)
• cannot be determined from g(x) = intg{ f(x) dx }
•   must be given in addition to g(x) = intg{ f(x) dx }
• both of these
5. Given: g(x) = intg{ f(x) dx }. The intg_a_b{ f(x) dx } is the change in ___ between x=a and x=b.
g(x)
6. Y = intg_a_b{ f(x) dx }. Y is a
number
7. Y = intg_a_b{ f(x) dx }. If Y is negative, then f(x) was primarily _____ the x axis.
below
8. Y = intg_a_b{ f(x) dx }. If Y is positive, then f(x) was primarily _____ the x axis.
above
9. Y = intg_a_b{ f(x) dx }. Area above or below f(x) means
area between the function and the x axis
10. Y = intg_a_b{ f(x) dx }. Y is the area _____ between x=a and x=b.
above f(x) or below f(x)
11. intg_a_b{ f(x) dx }, is known as a(n)
definite integral
12. In Y = intg_a_b{ f(x) dx }. Y is
a number, which is the area bounded by the function and the x axis
13. In intg_a_b{ f(x) dx }, b is the _____ limit of integration.
upper
14. In intg_a_b{ f(x) dx }, a is the _____ limit of integration.
lower`
15. In intg_a_b{ f(x) dx }, the limits of integration are x=
a and b
16. In intg{ f(x) dx }, f(x) is a function. Can f(x) have a constant value?
yes
17. In intg{ f(x) dx }, the independent variable is
x
18. intg{ f(x) dx } means integral of the function f(x) with respect to x.
true
19. The definite integral of a function is
number
20. Integral operator is a(n) _______ operator
area
21. The indefinite integral of a function is
a function
22. The definite integral of a function is
area (a number) under/over the function
23. The integral of a constant is
not defined
24. One way to remember which axis is the abscissa and ordinate is the shape of the mouth when saying the words.
true
25. Ordinate is the
y-axis
26. Abscissa is the
x-axis
27. h=cos x; intg{ h dx } = ______ at x=pi/2 if C=2.
3
28. h=cos x; intg{ h dx } = ______ at x=pi/2 if C=1.
2
29. h=cos x; intg{ h dx } = ______ at x=pi/2 if C=0
1
30. h'=cos x; h(pi)=
0
31. h'=cos x; h(pi/2)=
1
32. h'=cos x; h(0)=
0
33. h=sin x; h'(pi)=
-1
34. h=sin x; h'(pi/2)=
0
35. h=sin x; h'(0)=
1
36. The relationship indicated in fig 9060-B is
dL^2 = dx^2 + dy^2
37. Differential area in fig 9060-C is
y*dx
38. The surface area indicated in fig 9060-D is formed by rotating ____ about the ___ axis
y(x), x
39. Fig 9060-E shows the differential area dA =
2*pi*y*dL
40. Fig 9060-F shows the differential volume dV =
pi*y^2*dx
41. The volume indicated in fig 9060-D is formed by rotating ____ about the ___ axis.
y(x), x
42. Fig 9060-E shows the differential area dA =
2*pi*y*dL
43. The relationship indicated in fig 9060-B is
dL^2 = dx^2 + dy^2
44. Differential length in fig 9060-A is
dL
45. The volume of a y(x) with apex at the origin is V = integ{ dV } and dV= pi*y^2*dx which is a differential volume of a ______ in Fig9060F.
cylinder
46. The surface area of any y(x) rotated about the x axis with apex at the origin is A = integ{ dA }, where dA=______ in Fig9060E.
2*pi*y*dL
47. The surface area of a cone with apex at the origin and cone axis is along the x-axis is A = integ{ dA } and dA=
2*pi*y*dL
48. If the function y(x) is rotated about the x axis in Fig9060D, then ________ is generated.
an enclosed volume and surface area
49. If the function y(x)=2x is rotated about the x axis, then ________ is generated for positive x.
cone
50. If the function y(x)=3x^2 is rotated about the x axis, then ________ is generated for positive x.
a horn
51. A=intg{dA} means integrate over all differential areas or add-up all the area segments, where dA=y*dx in Fig9060C. Classical integration (vs numerical integration) is possible when the function y(x) is known.
true
52. A=intg{dA} means integrate over all differential areas or add-up all the area segments, and dA=y*dx where dx in Fig9060C means
rectangle width
53. A=intg{dA} means integrate over all differential areas or add-up all the area segments, and dA=y*dx where y in Fig9060C means
distance from the x-axis to the function y(x) in the y direction
54. A=intg{dA} means integrate over all differential areas or add-up all the area segments, where dA=y*dx in Fig9060C is the area of a
rectangle of height y and width dx
55. A=intg{dA} means integrate over all differential areas or add-up all the area segments, where A means
area
56. A=intg{dA} means integrate over all differential areas or add-up all the area segments, where dA means
• all of these
• differential area
• delta area
• smallest-possible area segment
57. Draw the right triangle: dx along the x axis; dy along the y axis; and dL along the hypotenuse. Write the pythagorean equation in Fig9060B. Divide by dx^2. dL=
sqrt(1+y'*y')*dx
58. L=intg{dL} means integrate over all differential lengths or add-up all the length segments, where dL= ______ using Fig9060B.
sqrt(1+y'*y')*dx
59. L=intg{dL} means integrate over all differential lengths or add-up all the length segments, where L means total
length
60. L=intg{dL} means integrate over all differential lengths or add-up all the length segments, where dL in Fig9060A means
• all of these
• differential length
• delta length
• smallest-possible length segment
61. In a right-hand coordinate system,
ixj = k
62. 2. A function that produces a 3D surface is z(x,y), which means that z is a function of
x and y
63. 3. The number of slopes for any point on a 3D surface is
infinite
64. 4. When one takes a derivative of a 3D surface, the direction of the derivative
must also be specified
65. The derivative of z(x,y) with y held constant is the ____ derivative of z with respect to ____.
partial, x
66. The derivative of z(x,y) with x held constant is the ____ derivative of z with respect to ____.
partial, y
67. Partial derivatives are meaningful for 3D surfaces
true
68. Partial derivative of z(x,y) with respect to x is the same a regular derivative except ___ is considered constant.
y
69. Partial derivative of z(x,y) with respect to y is the same a regular derivative except ___ is considered constant.
x
70. The number of tangent planes for any point on a 3D surface is
one
71. The number of tangent lines for any point on a surface is
infinite
72. The number of lines that define a plane is
two
73. z(x,y) = f(x,y). A common notation of partial derivative of f with respect to x is
fx
74. z(x,y) = f(x,y). A common notation of partial derivative of f with respect to y is
fy
75. The derivative of z(x,y) can be the partial derivative of z with respect to x, because ___ is held constant.
y
76. The derivative of z(x,y) can be the partial derivative of z with respect to y, because ___ is held constant.
x
77. . Engineers often encounter laboratory data (x0,y0; x1,y1; ... xn,yn), where y is a function of x. The function y that passes exactly through all the data points ____ well-known standard function.
will probably not match any
78. Laboratory data (x,y pairs of numbers) might reflect some well-known standard function, but will never match exactly because of
all of these
79. Laboratory data (x,y pairs of numbers) can be numerically integrated (approximated) by
• all of these and many others
• Simpson's method
• backward integration
• forward integration
• trapezoidal integration
80. Forward integration is the area of
rectangles
81. Backward integration is the area of
rectangles
82. Trapezoidal integration is the area of
trapezoids
83. Simpson's integration is the area under
parabolas
84. The average of forward and backward integration is ____ integration.
trapezoidal
85. (y0/2 + y1 + y2 + ... + yn/2)*delta-x is the formula for _____ integration.
trapezoidal
86. (y1 + y2 + ... + yn)*delta-x is the formula for ______ integration. Note the first point (y0) is not used.
backward
87. (y0 + y1 + ... + y(n-1))*delta-x is the formula for ______ integration. Note the last point (yn) is not used.
forward
88. (2*sum_of_all_y's - y0/2 -yn/2)*delta-x is the formula for _____ integration. Add all the y's; multiply by 2; subtract half the first and last; multiply by delta-x.
trapezoidal
89. (y0+4y1+2y2+4y3+2y4+...+2y(n-2)+4y(n-1)+yn)*delta-x/3 is the formula for ____ integration.
Simpson's
90. The number of data points permitted in Simpson's integration is
odd (n=even)
91. The number of data points permitted in trapezoidal integration is
either odd or even
92. The number of data points permitted in backward or forward integration is
either odd or even
93. Numerical integration can be implemented with forward, backward, trapezoidal, and Simpson's integration in any computer or calculator.
true
94. Numerical integration can be implemented with MS Excel using forward, backward, trapezoidal, and Simpson's integration. The most difficult would be:
Simpson's
95. Engineers often encounter laboratory data (x0,y0; x1,y1; ... xn,yn), where y is a function of x. Any one of the standard functions can be forced to approximate the data.
true
96. The feature in Excel called ____ can be used to force a standard function to approximate any set of laboratory data (x0,y0; x1,y1; ... xn,yn).
trend line
97. Start to add a trendline to an Excel graph by
clicking on one of the data points
 Author: lacythecoolest ID: 310219 Card Set: ENT 300 exam II Updated: 2015-11-30 17:37:14 Tags: Engineering math Folders: Description: pre class quizzes for exam II Show Answers: