ENT 300 exam II

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lacythecoolest
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310219
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ENT 300 exam II
Updated:
2015-11-30 12:37:14
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Engineering math
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pre class quizzes for 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

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