Module 23 - Answers | ||||
Lesson 1 | ||||
Answer 1 | ||||
23.1.1
The values of t are restricted to nonnegative values and because x = t the values of x are also restricted to those values. |
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Answer 2 | ||||
23.1.2
Swapping x and y produces the inverse relation whose graph is the original graph reflected across the line y = x.
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Answer 3 | ||||
23.1.3
[0, 2 ] x [-4, 4] x [-2, 2] The first interval given in the window coordinates above represents t-values, the second and third intervals represent x and y-values, respectively. |
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Answer 4 | ||||
23.1.4
The number of petals is N - 1 in the epicycloid x = N sin t - sin N t y = N cos t - cos N t |
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Lesson 2 | ||||
Answer 1 | ||||
23.2.1 dydx(0.5) = 2.08583, which agrees with the value found using the "Derivative" feature of the Graph screen. | ||||
Answer 2 | ||||
23.2.2 The slope of the tangent line when t = 2 is dydx(2) 0.642093 | ||||
Answer 3 | ||||
23.2.3
The window shown is [- , ] x [-3, 3] x [-5, 5]. The equation of the tangent to the curve when t = 2 is y 0.642093x + 0.715815. |
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Lesson 3 | ||||
Answer 1 | ||||
23.3.1 The arc length is 3/2 units. | ||||
Self Test | ||||
Answer 1 | ||||
Answer 2 | ||||
1/2 | ||||
Answer 3 | ||||
7/4 | ||||
Answer 4 | ||||
y = 0.5x 0.25 | ||||
Answer 5 | ||||
3.34122 units | ||||
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