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(a) Find the points on the polar curve r = 2(1 – cos(0)) where the tangents are horizontal. (b) Find the points on the polar curve r = 2(1 - cos(0)) where the tangents are vertical. (c) Find the length of the curve. FIGURE 3. r = 2(1 - cos(O)).
3 TT Find the slope of the tangent line to polar curve r = 7 – 6 sin 0 at the point ( 7 – 6- 2 2 3 TT TT Find the points (x, y) at which the polar curve r = 1 + sin(e), 0 < has a vertical 4 4. and horizontal tangent line. Vertical Tangent Line: Horizontal Tangent Line:
Find the area of the surface generated by revolving the equation r-2+2cos(0) about the polar axis. Find the length of the curve r 6; from 8-0 to θ
Find the area of the surface generated by revolving the equation r-2+2cos(0) about the polar axis. Find the length of the curve r 6; from 8-0 to θ
Question 1
(1 point) Find the length of the spiraling polar curve r = 3e60 From 0 to 21 . The length is (1 point) Find the area of the region that is bounded by the curve r = V6 sin(0) and lies in the sector 0 Sost. Area =
(1 point) Find the length of the spiraling polar curve r = 5e30 From 0 to 21. The length is
Find the exact length of the polar curve. r=θ₂, 0≤θ≤π/2
Find the slope of the tangent line to the polar curve: r = = 2 cos 6, at 0 = 1 Find the points on r = 3 cos where the tangent line is horizontal or vertical.
1. How do you find the area of a region bounded by a polar curve? 2. How do you find the length of a polar curve 3. Find the area of the circle given by r = sin 0 + cos 0. Check your result by converting the polar equation to rectangular form, then using the formula for the area of a circle.
Find the slope of the tangent line to the polar curve: r = 2 cos 6, at 0 = 1 Find the points on r = 3 cose where the tangent line is horizontal or vertical.
Find the slope of the polar curve of the cardiod r=-1+sin 0; 0 = 2