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he polar function Find a formula for the derivative r =1-cos(O), 05021. (4 points) Set up,...
only do part (a) 21. Graph the following polar curves: a) r = 2 + 4...
only do part (a)
21. Graph the following polar curves: a) r = 2 + 4 cos(O) b) r = 5 – 10 sin(0) For each of the graphs above, set up the integral(s) that calculates: the area of inner loop; • the area of outer loop; • the area between loops; the arclength of the inner loop; the arclength of the outer loop.
1. Set up, but do not evaluate, an integral to find the area enclosed by the...
1. Set up, but do not evaluate, an integral to find the area enclosed by the x-axis and the [x = 1 + et curve ly = t-t2 2. {*5+?2t Osts2 y = VE (1) Find the equation of the tangent line at the point where t = (2) Set up, but do NOT evaluate, an integral to find the area of the surface obtained by rotating the curve about the y-axis. 3. Set up but do NOT evaluate an...
Below is a graph of the circle r = 4 cos θ and the circle r...
Below is a graph of the circle r = 4 cos θ and the circle r = 2.
y x −1 1 −2 2 −2 −1 1 2 3 4 (i) Find the polar coordinates of both
intersection points of these two curves. (Note: show all of your
work) (ii) Set up (but do not evaluate) an integral that represents
the area inside of the circle r = 4 cos(θ) and outside of the
circle r = 2. (Note: no...
(a) Find the points on the polar curve r = 2(1 – cos(0)) where the tangents...
(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)).
s(100) 10.Find the area enclosed by the polar curve r = 5 cos 10 12.57T 257T...
s(100) 10.Find the area enclosed by the polar curve r = 5 cos 10 12.57T 257T 11. Determine whether the series is convergent or divergent by expressing it as a its sum telescoping sum. If it is convergent, find 00 In n+1 n=1 1 O In 2 -1 O The series is divergent. 12. Use the Comparison Test or the Limit Comparison Test to determine if the following series converges or diverges. 3 5 n=1 n5+5 converges diverges
s(100) 10.Find...
AME: 2. (24pts) Consider the curve given in polar coordinates by r-12 cos(0) Vsin(0), (0 0...
AME: 2. (24pts) Consider the curve given in polar coordinates by r-12 cos(0) Vsin(0), (0 0 < #). (i) Make a table of the values of the function f(0)--12 cos(0)/sin(0) /6 /4 n/3 5m/12 m/2 7m/12 2n/3 3n/4 5n/6 11 m/12 f(0) are to be rounded to two decimal places. (Hint. Given on 0, r); all the values f(0) an angle 9, enter the value of 0 to the variable C of your calculator, and then evaluate /(0) using the...
(1 point) Find the area of the inner loop of the Imacon with polar equation r-7 cos θ-2 =cos-1(3)...
(1 point) Find the area of the inner loop of the Imacon with polar equation r-7 cos θ-2 =cos-1(3) Answer: (1 point) Sketch the segment r-sec θ for 0 θ Then compute its length in two ways: as an integral in polar coordinates and using trigonometry
(1 point) Find the area of the inner loop of the Imacon with polar equation r-7 cos θ-2 =cos-1(3) Answer:
(1 point) Sketch the segment r-sec θ for 0 θ Then compute its length...
8. a) Set up the integral you would need to evaluate to find the length of...
8. a) Set up the integral you would need to evaluate to find the length of the curve given in #3 if Osts6. b) Set up the integral you would need to evaluate to find the arclength of the curve r = 6 sin(30), traced out once. 6 5 41 31 21 11 -6 -5 -4 -3 -2 -1 HN 4 ふふふ
Set up and evaluate the double integral using polar coordinates f(x,y) = 8-y; R is the...
Set up and evaluate the double integral using polar coordinates f(x,y) = 8-y; R is the region enclosed by the circles with polar equations r=cos(theta) and r=3cos(theta). I am struggling with understanding how to determine the interval for theta. The answer key says 0<= theta <= pi but I don't understand why. Please elaborate on this when solving.
shown that is a polar equations. r = 4 r. 8 cos e i) sketch two...
shown that is a polar equations. r = 4 r. 8 cos e i) sketch two curves on a single polar coordinate system. Shade the region enclosed by r, and ra. ii) Find the two intersection angles between r, and ra iii) Based on the answer i) and ii), find the shaded region's area.
only do part (a)
21. Graph the following polar curves: a) r = 2 + 4 cos(O) b) r = 5 – 10 sin(0) For each of the graphs above, set up the integral(s) that calculates: the area of inner loop; • the area of outer loop; • the area between loops; the arclength of the inner loop; the arclength of the outer loop.
1. Set up, but do not evaluate, an integral to find the area enclosed by the x-axis and the [x = 1 + et curve ly = t-t2 2. {*5+?2t Osts2 y = VE (1) Find the equation of the tangent line at the point where t = (2) Set up, but do NOT evaluate, an integral to find the area of the surface obtained by rotating the curve about the y-axis. 3. Set up but do NOT evaluate an...
Below is a graph of the circle r = 4 cos θ and the circle r = 2.
y x −1 1 −2 2 −2 −1 1 2 3 4 (i) Find the polar coordinates of both
intersection points of these two curves. (Note: show all of your
work) (ii) Set up (but do not evaluate) an integral that represents
the area inside of the circle r = 4 cos(θ) and outside of the
circle r = 2. (Note: no...
(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)).
s(100) 10.Find the area enclosed by the polar curve r = 5 cos 10 12.57T 257T 11. Determine whether the series is convergent or divergent by expressing it as a its sum telescoping sum. If it is convergent, find 00 In n+1 n=1 1 O In 2 -1 O The series is divergent. 12. Use the Comparison Test or the Limit Comparison Test to determine if the following series converges or diverges. 3 5 n=1 n5+5 converges diverges
s(100) 10.Find...
AME: 2. (24pts) Consider the curve given in polar coordinates by r-12 cos(0) Vsin(0), (0 0 < #). (i) Make a table of the values of the function f(0)--12 cos(0)/sin(0) /6 /4 n/3 5m/12 m/2 7m/12 2n/3 3n/4 5n/6 11 m/12 f(0) are to be rounded to two decimal places. (Hint. Given on 0, r); all the values f(0) an angle 9, enter the value of 0 to the variable C of your calculator, and then evaluate /(0) using the...
(1 point) Find the area of the inner loop of the Imacon with polar equation r-7 cos θ-2 =cos-1(3) Answer: (1 point) Sketch the segment r-sec θ for 0 θ Then compute its length in two ways: as an integral in polar coordinates and using trigonometry
(1 point) Find the area of the inner loop of the Imacon with polar equation r-7 cos θ-2 =cos-1(3) Answer:
(1 point) Sketch the segment r-sec θ for 0 θ Then compute its length...
8. a) Set up the integral you would need to evaluate to find the length of the curve given in #3 if Osts6. b) Set up the integral you would need to evaluate to find the arclength of the curve r = 6 sin(30), traced out once. 6 5 41 31 21 11 -6 -5 -4 -3 -2 -1 HN 4 ふふふ
shown that is a polar equations. r = 4 r. 8 cos e i) sketch two curves on a single polar coordinate system. Shade the region enclosed by r, and ra. ii) Find the two intersection angles between r, and ra iii) Based on the answer i) and ii), find the shaded region's area.
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