WA3 Clark.docx - Name Diana Clark University ID 0644492...

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Name: Diana Clark University ID: 0644492 Thomas Edison State University Calculus II (MAT-232) Section no.: WA3 Semester and year: September 2020 Written Assignment 3 Answer all assigned exercises, and show all work. Each exercise is worth 5 points. Section 9.1 2. Sketch the plane curve defined by the given parametric equations, and find an x - equation for the curve. y
y =− 2 + 2sin ( π 2 ) ¿ 0 t = 3 π 4 x = 1 + 2cos ( 3 π 4 ) ¿ 1 2 y =− 2 + 2sin ( 3 π 4 ) ¿ 2 + 2 t = π x = 1 + 2cos ( π ) ¿ 1 y =− 2 + 2sin ( π ) ¿ 2 t = 3 π 2 x = 1 + 2cos ( 3 π 2 ) ¿ 1 y =− 2 + 2sin ( 3 π 2 ) ¿ 4 t = 2 π x = 1 + 2cos ( 2 π ) ¿ 3 y =− 2 + 2sin ( 2 π ) ¿ 2 WA 3, p. 2
1 2cos 2 2sin x t y t    ( x 1 ) 2 + ( y + 2 ) 2 = 2 2 sin 2 t + 2 2 cos 2 t ( x 1 ) 2 + ( y + 2 ) 2 = 2 2 ( sin 2 t + cos 2 t ) ( x 1 ) 2 + ( y + 2 ) 2 = 2 2 8. Sketch the plane curve defined by the given parametric equations, and find an x - equation for the curve. y
12. Sketch the plane curve defined by the given parametric equations, and find an x - equation for the curve. y y
y = 1 x 2 22. Find parametric equations describing the given curve.
28. Find parametric equations describing the given curve.
Section 9.2 6. Find the slopes of the tangent lines to the given curves at the indicated points.
y dt = cos t t 2 + ¿ 1 t ¿ ¿ ¿ y x = ( y dt ) ( dx t ) = cos t ¿ a) t =− π = ( π ) + 1cos ( π ) π = π 2 + 1 π ( 1 ) Slope = π 2 + 1 π b) t = π = ( π ) 2 + 1cos ( π ) π = π 2 + 1 π ( 1 ) Slope = π 2 + 1 π c) ( 0,0 ) x = t 2 + 1 = 0 t 2 + 1 = 0 ( 0,0 ) does not belong to the curve so no such valve of t which satisfy (0,0) , so no slope 8.

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