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Q: Write the first-order linear differential equation in standard form. A) B) C) D) E)

Q: Solve the differential equation to find velocity v as a function of time t if when The differential equation models the motion of two people on a toboggan after consideration of the forces of gravity, friction, and air resistance. A) B) C) D) E)

Q: Find an equation of the graph that passes through the point and has the specified slope. Then graph the equation. Point: , Slope: A) B) C) D) E) None of the Above

Q: Use the initial condition to find the particular solution of the differential equation. , when A) B) C) D) E)

Q: The isotope has a half-life of 5,715 years. Given an initial amount of 11 grams of the isotope, how many grams will remain after 1,000 years? After 10,000 years? Round your answers to four decimal places. A) 6.8205 gm, 2.2896 gm B) 3.8974 gm, 1.3083 gm C) 9.7436 gm, 3.2708 gm D) 11.6923 gm, 3.9250 gm E) 5.8462 gm, 1.9625 gm

Q: Find the general solution of the differential equation A) B) C) D) E)

Q: Use separation of variables to find the general solution of the differential equation. A) B) C) D) E)

Q: Write the the differential equation by separating the variables. A) B) C) D) No, the variables cannot be separated E)

Q: Write the the differential equation by separating the variables. A) B) C) D) E)

Q: Some of the curves corresponding to different values of C in general solution of the differential equation are shown in the figure given below. Find the particular solution that passes through the points plotted on the graph. A) B) C) D) E)

Q: Use the integration to find the general solution of the differential equation . A) B) C) D) E)

Q: Find the general solution satisfies the differential equation. Then find the particular solution that satisfies the initial condition. General Solution: Differential equation: Initial condition: A) B) C) D) E)

Q: Determine whether the function is a solution of the differential equation .A) SolutionB) Not a solution

Q: Use integration to find a general solution of the differential equation . A) B) C) D) E)

Q: Use integration to find a general solution of the differential equation. A) B) C) D) E)

Q: Find the particular solution of the differential equation that satisfies the initial condition y = 8 when x = 3, where is the general solution. A) B) C) D) E)

Q: Which of the following is a solution of the differential equation ? A) B) C) D) E)

Q: Determine whether is a solution of the differential equation . A) B) C) D) E)

Q: Write the first five terms of the sequence. an = A) B) C) D) E)

Q: Write the first five terms of the sequence. an = A) B) C) D) E) none of the above

Q: The ordering and transportation cost C of the components used in manufacturing a product is given by where C is measured in thousands of dollars and x is the order size in hundreds. Find the order size that minimizes the cost. Round your answer to the nearest unit. A) 58 hundreds B) 56 hundreds C) 53 hundreds D) 55 hundreds E) 60 hundreds

Q: You are in a boat 2 miles from the nearest point on the coast (see figure). You are to go to a point Q, which is 3 miles down the coast and 1 mile inland. You can row at 8 miles per hour and walk at 9 miles per hour. Toward what point on the coast should you row in order to reach point Q in the least time? Round your answer to three decimal places. A) approximately 2.286 milesB) approximately 2.722 milesC) approximately 1.606 milesD) approximately 1.831 milesE) approximately 2.486 miles

Q: Use Newton's Method to find the point on the graph of that is closest to the point . Round your answer to three decimal places. A) B) C) D) E)

Q: Use Newton's Method to approximate . Round your answer to three decimal places. A) 0.714 B) 1.476 C) 2.597 D) 1.627 E) 2.000

Q: The value for which Newton's method fails for the function below is shown in the graph. Give the reason why the method fails. A) B) C) D) E)

Q: Use a graphing utility to approximate all the real zeros of the function by Newton's Method.A) -2.031, 3.236, 9.571B) -1.271, 2.028, 5.333C) -1.351, -1.471, -1.151D) -1.471, 3.236, 9.707E) -1.991, 2.970, 9.571

Q: Approximate, to three decimal places, the x-value of the point of intersection of the graphs of f(x) and g(x). Round your answer to three decimal places. A) 0.572B) 0.562C) 0.567D) 0.517E) 0.617

Q: Use Newton's Method to approximate the x-value of the indicated point intersection of the two graphs accurate to three decimal places. A) 0.371 B) 0.363 C) 0.356 D) 0.359 E) 0.352

Q: Use Newton's Method to approximate the zero(s) of the function accurate to three decimal places.A) 16.944B) 16.948C) -16.944D) -16.948E) 16.938

Q: Use Newton's Method to approximate the zero(s) of the function accurate to three decimal places.A) 0.755B) 0.759C) -0.755D) -0.759E) 0.748

Q: Use Newtons Method to approximate the zero(s) of the function accurate to three decimal places.A) -0.596B) 0.603C) 0.596D) -0.604E) 0.591

Q: Complete two iterations of Newtons Method for the function using the initial guess 1.7. A) 1.732463, 1.731851 B) 1.732493, 1.732251 C) 1.732493, 1.732151 D) 1.732353, 1.732051 E) 1.732143, 1.731951

Q: Determine the maximum error guaranteed by Taylor's Theorem with Remainder when the seventh-degree Taylor polynomial is used to approximate in the interval centered at 0. Round your answer to five decimal places. A) 0.02002 B) 0.00202 C) 0.00020 D) 0.00002 E) 0.05002

Q: Use the sixth-degree Taylor polynomial centered at zero for the function to approximate the integral . Round your answer to nearest ten thousandth. A) 0.7620 B) 0.7720 C) 1.0170 D) 0.7670 E) 0.5170

Q: Use the fifth-degree Taylor polynomial centered at c = 2 for the function to approximate . Round your answer to nearest ten thousandth. A) 0.5165 B) 0.5267 C) 0.5067 D) 0.4055 E) 0.4306

Q: Use the fourth-degree Taylor polynomial centered at for the function to approximate . Round your answer to nearest thousandth. A) 0.610 B) 0.607 C) 0.732 D) 0.718 E) 0.619

Q: Find the Taylor polynomials (centred at zero) of degree (a) 1, (b) 2, (c) 3, and (d) 4. A) B) C) D) E)

Q: Use a symbolic differentiation utility to find the fourth-degree Taylor polynomials (centred at zero) . A) B) C) D) E)

Q: Use a symbolic differentiation utility to find the Taylor polynomials (centred at zero) of degrees (a) 2, (b) 4, (c) 6, (d) 8. A) B) C) D) E)

Q: Find the Taylor polynomials (centred at zero) of degree (a) 1, (b) 2, (c) 3, and (d) 4. A) B) C) D) E)

Q: A Taylor polynomial approximation of is given below. Use a graphing utility to graph both functions. A)B)C)D)E)

Q: Find the third degree Taylor polynomial centered at c = 4 for the function. A) B) C) D) E)

Q: Find the third Taylor polynomial at for the given function. A) B) C) D) E)

Q: Differentiate the series for to find the power series for the function . A) B) C) D) E)

Q: Integrate the series for to find the power series for the function . A) B) C) D) E)

Q: Find the power series for the function using the power series for . A) B) C) D) E)

Q: Find the radius of convergence of where . A) 1 B) C) D) 8 E) 16

Q: Find the radius of convergence centered at for the following function. A) 3 B) 2 C) 0 D) 1 E)

Q: Apply Taylor's Theorem to find the power series centered at for the function . A) B) C) D) E)

Q: Find the radius of convergence of the series . A) 1 B) 4 C) 6 D) 8 E) 5

Q: Find the radius of convergence of the power series. A) B) 1 C) D) -1 E) 0

Q: Find the radius of convergence of the series . A) 14 B) 5 C) 1 D) 9 E) 8

Q: Find the radius of convergence of the power series. A) 0 B) 10 C) 20 D) 100 E)

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