2, (20 pts) Consider the polar curve r-2 + cos48 for 0 θ 2n (a) Graph this curve and determine the points farthest from the origin. What values of 8 give these points? (b) Determine the points clo...
all parts please PART II 7) (8 pts) Given the polar equation r = 6 sin θ, 0 θ π a) Graph and find the length of the graph geometrically. b) Find the length of the graph by integrating. 8.) (9 pts) Given the four-leaved rose r 2sin(26). a) Show the symmetries. b) Find the tangents of the leaf through the pole to determine the limits of integration. c) Find the area of one leaf. PART II 7) (8 pts)...
Let S be the region in the first quadrant bounded above by the graph of the polar curve r = cos θ and bounded below by the graph of the polar curve r= 20, as shown in the figure above. The two curves intersect when θ = 0.450. What is the area of S? (A) 0.232 (B) 0.243(C) 0.27 (D) 0.384
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
Find the exact length of the polar curve. r=θ₂, 0≤θ≤π/2
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...
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...
8 s) Sketch the polar curve: 5cos(40) Show a table of values (using multiples of Pi/12) and graph the curve on the polar grid provided. Your points from the table should be visible on the graph 9) Find the area enclosed by 3-sin(6) 8 s) Sketch the polar curve: 5cos(40) Show a table of values (using multiples of Pi/12) and graph the curve on the polar grid provided. Your points from the table should be visible on the graph 9)...
5. The graphs of the polar curves r-4 and r-3 + 2 cos θ are shown in the figure above. The curves intersect 3 (a) Let R be the shaded region that is inside the graph of r-4 and also outside the graph of r 34 2 cos θ, as shown in the figure above. Write an expression involving an integral for the area of R. (b) Find the slope of the line tangent to the graph of r :-3...
Question as above. Graph the curve C that is represented by r(t)-[t 2t also r'(0) and r() cos t], 0 2π. Graph (20 pts) 2. t (10 pts) (c) Find the length of the curve traced by r(t)-[t sint tcost t], 0StS T. (10 pts) 4. Graph the curve: r- Pl. Graph also the velocity and accerlaration vectors at t=0 and I. Give the speeds at the two times. Give the expressions for the normal and tangential components of the...
12 10. Find the area enclosed by the polar curve 2 11 cos (80). 11T Hide Elapsed: 0000 27 Instructions O22π 11. This question is worth 20 points. You must complete both parts. Parts (a) and (b) are not related and should be answered as separate, distinct problems. θ2,0 θ (a) (10 points) Graph the polar curve r (b) (10 points) Find the surface area given by rotating the curve ya froma1 to 3 about the z axis. 12. This...