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Study Resources (Calculus)

11.Sketch the graph of the equation:   a. d. b. e. c.   12.Sketch the graph of the equation:   a. d. b. e. none of the above c.   13.Find the points of intersection of the graphs of the equations:   a. b. c. d. e.   14.The table given below shows the Consumer Price Index (CPI) for selected years. Use the regression capabilities of a graphing utility to find a mathematical model of.
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  6.Use Green's Theorem to evaluate the integral for the path C: boundary of the region lying between the graphs of and .   a. b. c. d. e.   7.Use Green's Theorem to evaluate the integral for the path C:  .   a. b. c. d. e.   8.Use Green's Theorem to evaluate the line integral where C is .   a. b. c. d. e.   9.Use Green's Theorem to evaluate the line.
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  11.Use Stokes's Theorem to evaluate .Use a computer algebra system to verify your results. Note: C is oriented counterclockwise as viewed from above.   a. b. c. d. e.   12.Use Stokes's Theorem to evaluate  where and S is .Use a computer algebra system to verify your result.   a. b. c. d. e.   13.Use Stokes's Theorem to evaluate    where.
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MULTIPLE CHOICE 1.Estimate the slope of the line from the graph.   a. b. 5 c. 2 d. e.   2.Sketch the line passing through the point (3, 4) with the slope .   a. d. b. e. c.   3.Find the slope of the line passing through the pair of points.   a. b. c. d. 0 e.   4.Find the slope of the line passing through the points and .   a. 63 b. 21 c. 42 d. 21 e. 42   5.If a line has slope .
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11.Determine whether y is a function of x.   a. no b. yes   12.Determine whether y is a function of x.   a. no b. yes   13.Use the graph of given below to find the graph of the function .   a. d. b. e. c.   14.Use the graph of given below to find the graph of the function .   a. d. b. e. c.   15.Specify a sequence of transformations for the function.
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21.Write the following expression in algebraic form.   a. b. c. d. e.   22.Write the following expression in algebraic form.   a. b. c. d. e.   23.Write the following expression in algebraic form.   a. b. c. d. e.   24.Solve the following equation for .   a. b. c. d. e.   25.Solve the following equation for .   a. b. c. d. e.       .
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MULTIPLE CHOICE 1.Find the curl of the vector field .   a. b. c. d. e.   2.Find the curl of the vector field   a. b. c. d. e.   3.Find the curl of the vector field   a. b. c. d. e.   4.Find the curl of the vector field   a. b. c. d. e.   5.Verify Stokes's Theorem by evaluating as a line integral and as a double integral .   a. b. c. d. e.     .
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6.Find the domain and range of the function .   a. domain: range: b. domain: range: c. domain: range: d. domain: range: e. domain: range:   7.Find the domain and range of the function .   a. domain: range: b. domain: range: c. domain: range: d. domain: range: e. none of the above   8.Find the domain and range of the function .   a. domain: range: b. domain: range: c. domain:.
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16.Write an equation of the line that passes through the given point and is perpendicular to the given line.   a. b. c. d. e.   17.Write an equation of the line that passes through the given point and is parallel to the given line.   a. b. c. d. e.   18.Write an equation of the line that passes through the point and is.
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MULTIPLE CHOICE 1.Match the following vector-valued function with its graph.   a. d. b. e. c.   2.Match the following vector-valued function with its graph.   a. d. b. e. c.   3.Find the rectangular equation for the surface by eliminating parameters from the vector-valued function. Identify the surface.   a. b. c. d. e.   4.Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function .   a. b. c. d. e.   5.Identify the surface by.
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MULTIPLE CHOICE 1.Determine which type of function would be most appropriate to fit the given data.   a. exponential b. linear c. quadratic d. no relationship e. trigonometric   2.Which function below would be most appropriate model for the given data?   a. no apparent relationship between x and y b. trigonometric c. quadratic d. linear   3.The following ordered pairs represent temperatures in degrees Fahrenheit taken each hour from 1:00 pm until 5:00 pm..
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MULTIPLE CHOICE 1.Match the graph of the function given below with the graph of its inverse function.   a. d. b. e. c.   2.Match the graph of the function given below with the graph of its inverse function.   a. d. b. e. c.   3.Use the Horizontal Line Test to determine whether the following statement is true or false. The function is one-to-one on.
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  11.Use Divergence Theorem to evaluate  and find the outward flux of  through the surface S of the solid bounded by   a. b. c. d. e. 0   12.Use Divergence Theorem to evaluate and find the outward flux of  through the surface S of the solid bounded by the planes   a. b. c. d. e.   13.Use Divergence Theorem to.
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15.Use Divergence Theorem to evaluate  and find the outward flux of through the surface S of the solid bounded by  and .   a. b. c. d. e.   16.Evaluate , where and S is the closed surface of the solid bounded by the graphs ,, and the coordinate planes.   a. b. c. d. e.   17.Evaluate where S is the closed surface.
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  16.Find the area of the surface over the given region. Use a computer algebra system to verify your results. The sphere,     a. b. c. d. e.   17.Find the area of the surface over the given region. Use a computer algebra system to verify your results. The part of the cone,   where .   a. b. c. d. e.   18.Find the area of the surface of revolution.
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15.Use Stokes's Theorem to evaluate Use a computer algebra system to verify your results. Note: C is oriented counterclockwise as viewed from above.   a. b. c. d. e.   16.Use Stokes's Theorem to evaluate  where  and S is the first-octant portion of over . Use a computer algebra system to verify your result.   a. b. c. d. e.   17.The.
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MULTIPLE CHOICE 1.Evaluate , where .   a. b. c. d. e.   2.Evaluate , where .   a. b. c. d. e.   3.Evaluate , where S is , first octant.   a. b. c. d. e.   4.Use a computer algebra system to evaluate where S is . Round your answer to two decimal places.   a. 124.82 b. 1.07 c. 62.41 d. 141.01 e. 64.00   5.Use a computer algebra system to evaluate where S is . Round your answer to two decimal.
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  11.Find a vector-valued function whose graph is the part of the paraboloid that lies inside the cylinder .   a. b. c. d. e.   12.Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function about the given axis.   a. b. c. d. e.   13.Write a set of parametric equations for the surface of.
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  6.Evaluate along the path C, defined as y-axis from . a. b. c. d. e.   7.Find the total mass of the wire with density .   a. b. c. d. e.   8.Evaluate where C is represented by .   a. b. c. d. e.   9.Evaluate where C is represented by .   a. b. c. d. e.   10.Find the work done by the force field on a particle moving along the given path. .
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6.Find all interce   a. x-interce   b. x-intercept: (0, 0); y-interce   c. x-interce   d. x-interce   e. x-interce     7.Find all interce   a. x-interce   b. x-interce   c. x-interce   d. x-interce   e. x-interce     8.Test for symmetry with respect to each axis and to the origin.   a. symmetric with respect to the origin b. symmetric with respect to the x-axis c. symmetric with respect to the y-axis d. no symmetry e. A, B, and C   9.Test for symmetry with respect to each axis and to the origin.   a. symmetric with.
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MULTIPLE CHOICE 1.Use the Divergence Theorem to evaluate Verify your answer by evaluating the integral as a triple integral. S: cube bounded by the planes   a. b. c. d. e.   2.Let and let S be the cylinder Verify the Divergence Theorem by evaluating as a surface integral and as a triple integral.   a. b. c. d. e.   3.Let  .
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16.Given and , evaluate .   a. b. c. d. e.   17.Determine whether the function is even, odd, or neither.   a. odd b. even c. neither   18.Determine whether the function is even, odd, or neither.   a. even b. odd c. neither   19.Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even.   a. b. c. d. e.       .
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  6.Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function and sketch the graph.   a. d. b. e. c.   7.Find a vector-valued function whose graph is the plane . a. b. c. d. e.   8.Find a vector-valued function whose graph is the cone .   a. b. c. d. e.   9.Find a vector-valued function whose graph is the cylinder .   a. b. c. d. e.   10.Find a vector-valued function.
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MULTIPLE CHOICE 1.Verify Green's Theorem by evaluating both integrals for the path C defined as the boundary of the region lying between the graphs of and .   a. b. c. d. e.   2.Verify Green's Theorem by setting up and evaluating both integrals for the path C: square with vertices (0,0), (10,0), (10,10), (0,10).   a. b. c. d. e.   3.Use Green's Theorem to.
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  6.Find the value of the line integral . (Hint: If is conservative, the integration may be easier on an alternate path.)   a. 243 b. 192 c. 108 d. 0 e. 12   7.Find the value of the line integral . (Hint: If is conservative, the integration may be easier on an alternate path.)   a. b. c. d. e.   8.Find the value of the line integral where C.
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MULTIPLE CHOICE 1.Which of the following is the correct graph of ?   a. d. b. e. c.   2.Which of the following is the correct graph of ?   a. d. b. e. c.   3.Which of the following is the correct graph of ?   a. d. b. e. c.   4.Which of the following is the correct graph of ?   a. d. b. e. c.   5.Find all interce   a. x-interce   b. x-intercept: (12, 0); y-interce   c. x-interce   d. x-interce   e. x-intercept: (, 0); y-intercept: (0, –12)       .
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16.Use the functions to find the function .   a. b. c. d. e.   17.Use the functions to find the function .   a. b. c. d. e.   18.Evaluate the expression without using a calculator.   a. 0 b. c. d. e.   19.Evaluate the expression without using a calculator.   a. b. c. d. e.   20.Evaluate the expression without using a calculator.   a. b. c. 3 d. 5 e. 4       .
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15.Evaluate the line integral using the Fundamental Theorem of Line Integrals, where C is the smooth curve from to .   a. 274 b. 298 c. 300 d. 30 e. 272   16.Find the work done by the force field in moving an object from P to Q.     a. 27,992 b. 55,985 c. 83,978 d. 41,989 e. 69,982   17.A stone weighing 2 pounds is attached to the end of a four-foot.
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MULTIPLE CHOICE 1.Evaluate (if possible) the function at . Simplify the result.   a. –7 b. 17 c. 3 d. 7 e. undefined   2.Evaluate (if possible) the function at . Simplify the result.   a. b. c. d. e.   3.Evaluate (if possible) the function at . Simplify the result.   a. b. c. d. e. none of the above   4.Let . Then simplify the expression .   a. b. c. d. e. undefined   5.Let . Evaluate the expression and then simplify.
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MULTIPLE CHOICE 1.Find a piecewise smooth parametrization of the path C given in the following graph.   a. b. c. d. e.   2.Find a piecewise smooth parametrization of the path C given in the following graph.   a. b. c. d. e.   3.Evaluate the line integral along the path C given by , where .   a. b. c. d. e.   4.Evaluate the line integral along the given path.   a. b. c. d. e.   5.Evaluate along the.
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