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25 Determine the surface of the solid formed by revolving the upper half of the circle x² + y² = p² about the x-axis

25 Determine the surface of the solid formed by revolving the upper half of the circle x² + y² = p² about the x-axis

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.6: Parametric Equations
Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...
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In this question p=6
Q5 Q6 Q7 Determine the surface of the solid formed by revolving the upper half of the circle x² + y² = p² about the x-axis Determine whether diverges. 2p ∞ √p+81n4 √p+81n² 8p+p²n+n² 8p+n+p² n=0 + Converges or i. Comment whether the sequence is Converges or diverges. ii. Obtain the first five terms of that sequence. 3p 2 Р , (P + ²/₁) n+ 1
Transcribed Image Text:Q5 Q6 Q7 Determine the surface of the solid formed by revolving the upper half of the circle x² + y² = p² about the x-axis Determine whether diverges. 2p ∞ √p+81n4 √p+81n² 8p+p²n+n² 8p+n+p² n=0 + Converges or i. Comment whether the sequence is Converges or diverges. ii. Obtain the first five terms of that sequence. 3p 2 Р , (P + ²/₁) n+ 1
Q1 Q2 Q3 Q4 Consider the plane curve defined by the parametric equations x = 2 + 2 cos² (t), y = 3+ sin(2t) Calculate the Arc length of the curve over the domain 0≤t≤pπ Find the area of the region included between the parabola py² = x and the line x + y = p. Calculate the area of the shaded region in the given figure y Parabola curve Focus point p- 2p 8p 0.5p Calculate the volume of the solid obtained by rotating the region bounded by the parabola y = x(2 − x) and the straight line y = 0 around the x-axis
Transcribed Image Text:Q1 Q2 Q3 Q4 Consider the plane curve defined by the parametric equations x = 2 + 2 cos² (t), y = 3+ sin(2t) Calculate the Arc length of the curve over the domain 0≤t≤pπ Find the area of the region included between the parabola py² = x and the line x + y = p. Calculate the area of the shaded region in the given figure y Parabola curve Focus point p- 2p 8p 0.5p Calculate the volume of the solid obtained by rotating the region bounded by the parabola y = x(2 − x) and the straight line y = 0 around the x-axis
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