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  6.Use the properties of summation and Theorem 5.2 to evaluate the sum.   a. 1156 b. 1190 c. 2108 d. 2244 e. 323   7.Use the properties of summation and Theorem 5.2 to evaluate the sum.   a. 9,176 b. 10,471 c. 18,907 d. 9,139 e. 98,346   8.Use the properties of summation and Theorem 5.2 to evaluate the sum.   a. 239 b. 7,656 c. 7,612 d. 3,861 e. 7,590   9.Use the properties of summation and Theorem 5.2 to evaluate the sum.   a. 2,156 b. 64,262 c. 68,057 d. 258,060 e. 66,033   10.Use left endpoints and 10 rectangles.
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MULTIPLE CHOICE 1.Evaluate the following definite integral by the limit definition.   a. b. c. d. e.   2.Evaluate the following definite integral by the limit definition.   a. 4375 b. c. 4372 d. 1125 e.   3.Evaluate the following definite integral by the limit definition.   a. –216 b. 240 c. –240 d. 192 e. 216   4.Write the following limit as a definite integral on the interval [2 , 5], where ci is any point in the ith subinterval.   a. b. c. d. e.   5.Write the limit.
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MULTIPLE CHOICE 1.Determine the open intervals on which the graph of is concave downward or concave upward.   a. concave downward on b. concave upward on ; concave downward on c. concave upward on ; concave downward on d. concave upward on e. concave downward on ; concave upward on   2.Determine the open intervals on which the.
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  6.Approximate the positive zero(s) of the function to three decimal places. Use Newton's Method and continue the process until two successive approximations differ by less than 0.001.   a. b. c. d. e.   7.Use Newton´s Method to approximate the x-value of the indicated point of intersection of the two graphs accurate to three decimal places.Continue the.
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  16.Find all relative extrema of the function . Use the Second Derivative Test where applicable.   a. relative max: ; no relative min b. relative min: ; no relative max c. relative min: ; no relative max d. relative max: ; no relative min e. no relative max or min   17.Find all relative extrema of the function . Use the Second Derivative.
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MULTIPLE CHOICE 1.Use the graph of the function   given below to estimate the open intervals on which the function is increasing or decreasing.   a. increasing on ; decreasing on b. increasing on ; decreasing on c. increasing on ; decreasing on d. increasing on ; decreasing on e. increasing on ; decreasing on   2.Identify the open.
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  11.Find the points of inflection and discuss the concavity of the function on the interval .   a. no inflection points. concave up on b. concave upward on ; concave downward on ; inflection point at c. no inflection points. concave down on d. concave downward on ; concave upward on ; inflection point.
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  16.Sketch the graph of the relation using any extrema, intercepts, symmetry, and asymptotes.   a. d. b. e. c.   17.A business has a cost of for producing x units. The average cost per unit is Find the limit of as x approaches infinity. a. 333.3 b. 1 c. 500 d. 0 e. 1.5   18.The graph shows the temperature T, in degrees Fahrenheit, of molten.
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MULTIPLE CHOICE 1.Find the value of the derivative (if it exists) of the function at the extremum point .   a. b. c. d. 0 e. 1   2.Find the value of the derivative (if it exists) of at the indicated extremum.   a. is undefined. b. c. d. e.   3.Find the value of the derivative (if it exists) of the function at the extremum point.
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  16.Sketch the graph of  the function and locate the absolute extrema of the function on the interval .   a. left endpoint: absolute minimum right endpoint: absolute maximum b. left endpoint: absolute minimum right endpoint: absolute maximum c. left endpoint: absolute minimum right endpoint: absolute maximum d. left endpoint: absolute minimum right endpoint: absolute maximum e. left.
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  11.Find the limit.     a. b. c. 1 d. –6 e.   12.Find the limit.     a. b. c. 1 d. 7 e.   13.Sketch the graph of the function using any extrema, intercepts, symmetry, and asymptotes.   a. d. b. e. c.   14.Sketch the graph of the function using any extrema, intercepts, symmetry, and asymptotes.   a. d. b. e. c.   15.Sketch the graph of the relation using any extrema, intercepts, symmetry, and asymptotes.   a. d. b. e. c.     .
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  11.Find the open interval(s) on which the function is increasing in the interval Round numerical values in your answer to three decimal places.   a. increasing on: b. increasing on: c. increasing on: d. increasing on: e. increasing on:   12.Find the relative maxima of on the interval by applying the First Derivative Test. Round.
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  6.For the function , use a graphing utility to complete the table and estimate the limit as x approaches infinity.                 a. –6 b. 2 c. 6 d. 0 e. None of the above   7.Find the limit.     a. b. 3 c. d. –3 e. 5   8.Find the limit.     a. b. 2 c. 0 d. e.   9.Find the limit.   a. 1 b. 0 c. d. e. does not exist   10.Find the limit.     a. b. 1 c. 0 d. e.     .
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MULTIPLE CHOICE 1.Complete two iterations of Newton's Method for the function using the initial guess . Round your answers to four decimal places.   a. b. c. d. e.   2.Complete two iterations of Newton's Method for the function using the initial guess  . Round all numerical values in your answer to four decimal places.   a. b. c. d. e.   3.Use Newton´s Method.
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  11.Analyze and sketch a graph of the function   .   a. d. b. e. c.   12.Analyze and sketch a graph of the function   .   a. d. b. e. c.   13.Analyze the graph of the function . Determine any intercepts, relative extrema, points of inflection and asymptotes. Also determine where the graph is increasing or decreasing and concave up or concave down. Then identify.
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  6.Determine whether Rolle's Theorem can be applied to the function  on the closed interval . If Rolle's Theorem can be applied, find all numbers c in the open interval such that   a. Rolle's Theorem applies; c = 0 b. Rolle's Theorem applies; c. Rolle's Theorem applies; d. Rolle's Theorem applies; e. Rolle's Theorem does.
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MULTIPLE CHOICE 1.Match the function with one of the following graphs. a. d. b. e. c.   2.Match the function with one of the following graphs.   a. d. b. e. c.   3.Match the function with one of the following graphs.   a. d. b. e. c.   4.For the function , use a graphing utility to complete the table and estimate the limit as x approaches infinity.                   a. 0.8000 b. 1.8000 c. 1.2500 d. 2.2500 e. 0.2500   5.For the function.
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  6.Find all critical numbers of the function , .   a. b. c. d. e.   7.Find all critical numbers of of the function , .   a. b. c. d. e.   8.Locate the absolute extrema of the function on the closed interval .   a. absolute maximum: absolute minimum: b. absolute maximum:  absolute minimum: c. absolute maximum: absolute minimum: d. absolute maximum: absolute minimum: e. absolute maximum: absolute minimum:   9.Locate.
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MULTIPLE CHOICE 1.Assume that x and y are both differentiable functions of t . Find for the equation  .   a. b. c. d. e.   2.Assume that x and y are both differentiable functions of t. Find for the equation .   a. b. c. d. e.   3.A point is moving along the graph of the function such that centimeters per.
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  11.Locate the absolute extrema of the given function on the closed interval .   a. absolute max: (0, 0); absolute min b. absolute max: ; absolute min (0, 0) c. absolute max: ; absolute min d. absolute max: ; no absolute min e. no absolute max; absolute min:   12.Locate the absolute extrema of the function on the closed.
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  6.Find the differential dy of the function .   a. b. c. d. e.   7.Find the differential dy of the function .   a. b. c. d. e.   8.The measurement of the side of a square floor tile is 14 inches, with a possible error of inch. Use differentials to approximate the possible propagated error in computing the area of the square.   a. b. c. d. e.   9.The measurements.
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  11.The radius of a spherical balloon is measured to be 8 inches, with a possible error of 0.03 inch. Use differentials to approximate the maximum possible error in calculating the volume of the sphere. Round your answer to two decimal places.   a. b. c. d. e.   12.The radius of a spherical balloon is measured to be.
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  6.Find the open interval(s) on which is increasing or decreasing.   a. increasing on decreasing on b. increasing on decreasing on c. increasing on decreasing on d. increasing on decreasing on e. increasing on decreasing on   7.Find the relative extremum of by applying the First Derivative Test.   a. relative minimum: b. relative maximum:.
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MULTIPLE CHOICE 1.The graph of a function f is is shown below. Sketch the graph of the derivative .   a. d. b. e. c.   2.The graph of a function f is is shown below. Sketch the graph of the derivative .   a. d. b. e. c.   3.The graph of a function f is is shown below. Sketch the graph of the derivative .   a. d. b. e. c.   4.The graph.
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  6.Find the derivative of the function .   a. b. c. d. e.   7.Find the derivative of the function .   a. b. c. d. e.   8.Find the derivative of the function .   a. b. c. d. e.   9.Find the derivative of the function . a. b. c. d. e.   10.Find the slope-intercept form of the equation of the line tangent to the graph of .   a. b. c. d. e.     .
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  6.Find all points of inflection on the graph of the function .   a. b. c. d. e.   7.Find the points of inflection and discuss the concavity of the function.   a. inflection point at ; concave upward on ; concave downward on b. inflection point at ; concare downward on ; concave upward on c. inflection point at ; concave downward.
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MULTIPLE CHOICE 1.Find the sum given below.   a. 42 b. 44 c. 38 d. 50 e. 40   2.Find the sum given below.   a. 3 b. 33 c. 25 d. 67 e. 43   3.Find the sum given below.   a. b. c. d. e.   4.Use sigma notation to write the sum .   a. b. c. d. e.   5.Use the properties of summation and Theorem 5.2 to evaluate the sum.   a. 667 b. 552 c. 575 d. 1311 e. 391     .
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MULTIPLE CHOICE 1.Find the general solution of the differential equation below and check the result by differentiation.   a. b. c. d. e.   2.Find the general solution of the differential equation below and check the result by differentiation.   a. b. c. d. e.   3.Find the indefinite integral .   a. b. c. d. e. none of the above   4.Find the indefinite integral .   a. b. c. d. e.   5.Find the indefinite integral .   a. b. c. d. e.     .
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  6.Write the following limit as a definite integral on the interval where ci is any point in the subinterval.   a. b. c. d. e.   7.Write the limit , as a definite integral on the interval , where ci is any point in the subinterval.   a. b. c. d. e.   8.The graph of the function is given below. Which.
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  6.Analyze and sketch a graph of the function .   a. d. b. e. c.   7.Analyze and sketch a graph of the function .   a. d. b. e. none of the above c.   8.Determine the slant asymptote of the graph of  .   a. b. c. d. e. no slant asymptotes   9.Analyze and sketch a graph of the function  .   a. d. b. e. c.   10.Analyze and sketch a graph of the function   .   a. d. b. e. c.     .
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  21.Determine the x-coordinate(s) of any relative extrema and inflection points of the function .   a. relative minimum: ; no inflection points b. relative maximum:; inflection point: c. no relative maximum or minimum; inflection point: d. no relative extrema or inflection points. e. relative minimum: ; inflection point:   22.The graph of f is shown. Graph f, f' and f'' on.
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  11.Find the indefinite integral .   a. b. c. d. e.   12.Solve the differential equation.   a. b. c. d. e.   13.Solve the differential equation.   a. b. c. d. e.   14.Solve the differential equation.   a. b. c. d. e.   15.A ball is thrown vertically upwards from a height of ft with an initial velocity of ft per second. How high will the ball go? Note that the acceleration of the ball is given by.
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  11.Determine whether the Mean Value Theorem can be applied to the function on the closed interval [0,16]. If the Mean Value Theorem can be applied, find all numbers c in the open interval (0,16) such that .   a. MVT applies; b. MVT applies; 4 c. MVT applies; d. MVT applies; 8 e. MVT does not apply   12.Determine whether the.
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MULTIPLE CHOICE 1.Find an equation of the tangent line to the graph of at the point .   a. b. c. d. e.   2.Find at the point for the equation .   a. b. c. d. e.   3.Find at the point for the equation .   a. b. c. d. e.   4.Find the derivative of the function .   a. b. c. d. e.   5.Find the derivative of the function .   a. b. c. d. e.     .
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MULTIPLE CHOICE 1.Find two positive numbers whose product is 181 and whose sum is a minimum.   a. b. c. d. e.   2.Find two positive numbers such that the sum of the first and twice the second is 56 and whose product is a maximum.   a. b. 28 and 14 c. d. e.   3.Find the length and width of a rectangle that has perimeter .
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  11.Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral.   a. –158 b. 12 c. 80 d. 82 e. –160   12.Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral.   a. –1 b. 1 c. 2 d. 4 e. 15   13.Sketch the region whose area is given by the definite.
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  11.Use left endpoints and 12 rectangles to find the approximation of the area of the region between the graph of the function and the x-axis over the interval . Round your answer to four decimal places.   a. 0.0419 b. 0.1319 c. 0.1219 d. 0.0819 e. 0.0119   12.Find the limit of as .   a. 5/7 b. 5 c. 1/7 d. 10/7 e. unbounded   13.Find the limit of as .   a. 1/10 b. 5 c. unbounded d. 1/2 e. 1   14.The diagram.
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