5. (a) Give an equation in polar coordinates that represents the circle below y 4 4...
5. (a) Give an equation in polar coordinates that represents the circle below y 4 4 6 (b) Find the area contained within the circle given in part (a) by using the definite integral for area in polar coordinates Use the definition of the derivitive in polar coordinates to find the points, (,0), on the circle where vertical tangent lines exist
5. (a) Give an equation in polar coordinates that represents the circle below y 4 4 6 (b) Find the area contained within the circle given in part (a) by using the definite integral for area in polar coordinates Use the definition of the derivitive in polar coordinates to find the points, (,0), on the circle where vertical tangent lines exist
a- find equation in terms of polar coordinates that represent the figure b - determine the area contained within the circle given in part (a) by using tbe definite integral c- use def of the derivitive in polar coordinates to find points (r, (theta)) on the circle where vertical tangent line exists 4 OE 6 4 12 4 -4.
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...
Consider the polar graph r=1-sin theta and r= sin theta, shown below. Please help with B, D, and E 5. Consider the polar graphs r = 1-sin 0 and r = sin 0, shown below. a. Find the polar coordinates (r, 2) for all points of intersection on the figure. Hint: Not all points can be found algebraically. For b.-d., set up an integral that represents the area of the indicated region. b. The region inside of the circle, but...
Evaluate the given integral by changing to polar coordinates. ∫∫R(4x − y) dA, where R is the region in the first quadrant enclosed by the circle x2 + y2 = 4 and the lines x = 0 and y = x.
7. Evaluate the following integral by converting to polar coordinates: S], 127 (2x – y)dA, where R is the region in the first quadrant enclosed by the circle x2 + y2 = 4 and the lines x = 0 and y = x. 8. Find the surface area of the portion of the plane 3x + 2y +z = 6 that lies in the first octant. 9. Use Lagrange multipliers to maximize and minimize f(x, y) = 3x + y...
6) a) Find the area of the circle (x-3)+ y'- 9 using polar coordinates b) Find the area of the region below the cardioid r = 1 + cos(9) and above y = 1x1. 6) a) Find the area of the circle (x-3)+ y'- 9 using polar coordinates b) Find the area of the region below the cardioid r = 1 + cos(9) and above y = 1x1.
just make circle questions which 2,(b) and 3,(i) thank you 2. (Polar Coordinates: Polar Plots). (a) Consider the curve given in polar coordinates (i) Use a scientific calculator to fill in the following table with the (approximations of) values of the function r(0) on π, π r(e) (the approximations of the values r(e) must be good to at least two decimal places). (i) Use the graph paper for the polar coordinate system (attached to the assignment sheet) to plot the...
Problem 6 [5 points] |(y ( y-dan- 0.708 Set up an equation with a double Integral in polar coordinates to find a such that the volume inside the hemisphere z 16-x-yi and outside the cylinder x2 + y2 = a 2 is one-half the volume of the hemisphere. Do not solve it. Problem 6 [5 points] |(y ( y-dan- 0.708 Set up an equation with a double Integral in polar coordinates to find a such that the volume inside the...