Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 6.4, Problem 37PS
To determine
To find:The surface area generated by the polar curves
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44. A tangent at the pole to the polar curve r = 2- 4 sin 0
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44. A tangent at the pole to the polar curve r= 2-4 sin 0
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Chapter 6 Solutions
Calculus
Ch. 6.1 - Prob. 1PSCh. 6.1 - Prob. 2PSCh. 6.1 - Prob. 3PSCh. 6.1 - Prob. 4PSCh. 6.1 - Prob. 5PSCh. 6.1 - Prob. 6PSCh. 6.1 - Prob. 7PSCh. 6.1 - Prob. 8PSCh. 6.1 - Prob. 9PSCh. 6.1 - Prob. 10PS
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- 3. Which of the following is the equation of the tangent at the point 0 3 line to the polar curve r= se. V3 (a) 5. 3V3 (b) (c) V3 T+1 (d)arrow_forward11. Find the area within the curves y = 25 – x², 256x = 3y², and 16y = 9x?. C. 36.27 units? A. 37.26 units² B. 37.62 units? D. 32.67 units? sin20 12. Find the area bounded by the polar curve r = 16 sin0- 2 A. 16 sq. units B. 8 sq. units C. 4 sq. units D. 2 sq. units 13. The region bounded by y =x°, y = 0, and x = 2 is revolved about the line x = 2. Find the volume of t' 3/3 solid of revolution generated using disk method. A. 10.5031 units? B. 10.0531 units? C. 10.3501 units? D. 10.3051 units?arrow_forward24. Which of the folowing polar curves is a cardioid? A. r = cos? () B. r= 2+3sin0 C. r = 3 – 2cos0 D. r= cos () 25. What is the area of one of the petals of the rose curver = 2 cos(20)? - / cos"(20)d0 8/, cos"(20) do A. В. 8 -x/4 -x/4 지/4 4 cos"(20) do D. 2/ cos"(20) do r/4 C. J-x/4 */4arrow_forward
- 8. Find the area of the surface of revolution r = 2 cos 0 revolved about the π polar axis 0 < 0 <arrow_forwardPage 8 8. The curve y = Va-x with 0Sxs is rotated about the x-axis. Find the area of the resulting surface.arrow_forwardTrue or False. 1. If one uses the horizontal strip/element as a representative area, then the infinitesimal change may exist in either x or y variable depending on the orientation of the curve. 2. If a polar equation r = f (θ) is made θ = f (r), the limits of integration r1 and r2 must be obtained from the corresponding values of θ1, and θ2 which bound the area of concern. 3. The point (-13, -110π/4) is located between 0 and 1.80π region of a polar coordinate system and is identical to (13, 3π/2). 4. For any rose-petal curve in the form r = a cos(nθ) with the same maximum length a, the equation with the greater number of petals m, (m= n for odd, 2n for even) will always yield to larger area of the curve. 5. Any polar equation can be made rectangular. 6. The Theorem of Pappus will always be applicable to determine the volume of solid revolution for as long as the centroid of the figure and its distance from the axis of revolution are given. 7. The shell method is most applicable for…arrow_forward
- 4. a) Find the points of intersection of the polar curves r = 1 and r² = 2 sin(20) b) Find the area of the region that lies inside r² = 2 sin(20) but outside r = 1.arrow_forward44. The furthest point from the pole to the polar curve r = 2 + V2 sin 0 occurs when 0 = 2 в о C 2arrow_forward10. Consider the curve with polar equation r= 6 sin 0 where 0 < 0 < n . Without finding the Cartesian equation, determine the slope of the tangent line to the curve in the point where 0 = 1/6.arrow_forward
- 7. The polar equation of the curve r² + y? = 2x is r= 2 cos 0 T= sin 20 T= 2 sin 0 D r= cOs e B Carrow_forward12. (a) Sketch the curve in the polar coordinate system with directions, (b) Find the values of for the cardioid at which the tangent line is (i) vertical, (ii) horizontal. Show your work like we did in our class. r = -1+ cos(0).arrow_forward9. Find the slope of the tangent line to polar curve r = 9 cos 0 at the point 2' 3arrow_forward
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