Question

1. (1 pt) Use the SageMath cell below Exercise 1 in the online version of this lab to determine which of the following points lie on the curve e^x + sin(??y) + cos(x^2y) = x + y. Record your answer in the space below. (a) (0, 2) (b) (0, 1) (c) (1, 1) (d) (-1, 1/3) 2. (4 pts) For each of the following equations, use the SageMath cell below Exercise 2 in the online version of this lab to produce a plot of the implicit curve. If that plot indicates that y is not a function of x, explain in the space below why that is. Otherwise, explicitly write y as a function of x in the space below and use the online SageMath cell to produce a plot showing that the graph of your function and the implicit curve are the same. In either case, attach a printout of your plot(s) to this report. (a) 10xe^y - cos(x) = 6 Yes Y is a function of x, since it passes the vertical line test. y=ln((6+cos(x))/(10x)) (b) x^3(y^2 + 4) - x^4 = 2

          1. (1 pt) Use the SageMath cell below Exercise 1 in the online version of this lab to determine which of the following points lie on the curve e^x + sin(??y) + cos(x^2y) = x + y. Record your answer in the space below.
(a) (0, 2)
(b) (0, 1)
(c) (1, 1)
(d) (-1, 1/3)

2. (4 pts) For each of the following equations, use the SageMath cell below Exercise 2 in the online version of this lab to produce a plot of the implicit curve. If that plot indicates that y is not a function of x, explain in the space below why that is. Otherwise, explicitly write y as a function of x in the space below and use the online SageMath cell to produce a plot showing that the graph of your function and the implicit curve are the same. In either case, attach a printout of your plot(s) to this report.
(a) 10xe^y - cos(x) = 6
Yes Y is a function of x, since it passes the vertical line test. y=ln((6+cos(x))/(10x))
(b) x^3(y^2 + 4) - x^4 = 2

1. (1 pt) Use the SageMath cell below Exercise 1 in the online version of this lab to determine which of the following points lie on the curve e^x + sin(??y) + cos(x^2y) = x + y. Record your answer in the space below.
(a) (0, 2)
(b) (0, 1)
(c) (1, 1)
(d) (-1, 1/3)

2. (4 pts) For each of the following equations, use the SageMath cell below Exercise 2 in the online version of this lab to produce a plot of the implicit curve. If that plot indicates that y is not a function of x, explain in the space below why that is. Otherwise, explicitly write y as a function of x in the space below and use the online SageMath cell to produce a plot showing that the graph of your function and the implicit curve are the same. In either case, attach a printout of your plot(s) to this report.
(a) 10xe^y - cos(x) = 6
Yes Y is a function of x, since it passes the vertical line test. y=ln((6+cos(x))/(10x))
(b) x^3(y^2 + 4) - x^4 = 2

Added by Julie D.

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