1. Plot the following graphs in Cartesian coordinates. [2 = 4x0.5 each] a. y = x...

Transcribed Image Text:

1. Plot the following graphs in Cartesian coordinates. [2 = 4x0.5 each] a. y = x for -2 ≤ x ≤ 2. b. y = x for -2 ≤x≤ 2. c. y = (²-4) for -2 ≤x≤ 2. d. y = -√4-² for all x for which this is defined. 2. Plot the following implicitly defined curves. [2 = 4x0.5 each] a. x² + y² = 4 for all x and y for which this equation makes sense. b. xy = 1 for all x and y for which this equation makes sense. c. x² + 4y² = 4 for all x and y for which this equation makes sense. d. (x² + y²)² - 4x (x² + y²) - 4y² = 0 for all x and y for which this equation makes sense. 3. Plot the following parametric curves. [2 = 4x0.5 each] a. x = 2t and y 2t²2 for -1 <t≤1. b. x = 2 cos(t) and y = 2 sin(t) for 0 < t < 2. c. x=2 cos(t) and y = sin(t) for 0 ≤ t ≤ 2m. d. x = cos(4t) cos(t) and y = sin(3t) sin(t) for 0 ≤t≤ 2m. 4. Plot the following curves in polar coordinates. [2 = 4x0.5 each/ a. r= = 1 for 0 ≤ 0 ≤ 2. b. r = 2 cos(8) for 0 ≤ 0≤ 2. C. T= = cos(20) for 0≤0 ≤ 2. d. r= 2 (cos(0)-1) for 0 ≤ 0≤*. Some of the curves in questions 1-4 are part or all of other curves in questions 1-4. 1. Plot the following graphs in Cartesian coordinates. [2 = 4x0.5 each] a. y = x for -2 ≤ x ≤ 2. b. y = x for -2 ≤x≤ 2. c. y = (²-4) for -2 ≤x≤ 2. d. y = -√4-² for all x for which this is defined. 2. Plot the following implicitly defined curves. [2 = 4x0.5 each] a. x² + y² = 4 for all x and y for which this equation makes sense. b. xy = 1 for all x and y for which this equation makes sense. c. x² + 4y² = 4 for all x and y for which this equation makes sense. d. (x² + y²)² - 4x (x² + y²) - 4y² = 0 for all x and y for which this equation makes sense. 3. Plot the following parametric curves. [2 = 4x0.5 each] a. x = 2t and y 2t²2 for -1 <t≤1. b. x = 2 cos(t) and y = 2 sin(t) for 0 < t < 2. c. x=2 cos(t) and y = sin(t) for 0 ≤ t ≤ 2m. d. x = cos(4t) cos(t) and y = sin(3t) sin(t) for 0 ≤t≤ 2m. 4. Plot the following curves in polar coordinates. [2 = 4x0.5 each/ a. r= = 1 for 0 ≤ 0 ≤ 2. b. r = 2 cos(8) for 0 ≤ 0≤ 2. C. T= = cos(20) for 0≤0 ≤ 2. d. r= 2 (cos(0)-1) for 0 ≤ 0≤*. Some of the curves in questions 1-4 are part or all of other curves in questions 1-4.

Answer rating: 100% (QA)

Use SageMath in a Jupyter notebook en... View the full answer