These question are solved by following method.
2) Consider polar curre r=4coso and r=1+2 caso r=1+2 cos r=4coso B A a) Find ALL...
Find the slope of the tangent line to the polar curve: r = 2 cos 6, at 0 = 1 Find the points on r = 3 cose where the tangent line is horizontal or vertical.
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...
Find the slope of the tangent line to the polar curve: r = = 2 cos 6, at 0 = 1 Find the points on r = 3 cos where the tangent line is horizontal or vertical.
5. Consider the polar graphs, r = 1-sin θ and r = sin θ , shown in the figure below. Find the polar coordinates (r, θ) for all the points of intersection on the figure. a) b) Find the area of the region that lies inside both the graph of r-1-sin θ and Find the slope of the line tangent to the graph of r-1-sin θ at θ-- Find a Cartesian equation for the line tangent to the graph of...
1. The polar curves r@) = 1 + 2 sin(39), r = 2, are graphed below. 2 (a) Find the area inside the larger loops and outside the smaller loops of the graph of r 12 sin(30). [Hint: Use symmetry, the answer is 3v3.] [Answer: sf-i.] quadrant where r is maximum? (b) Find the area outside the circle r 2 but inside the curve r 1+2 sin(30) (c) What is the tangent line to the curve r-1+2sin(30) at the point...
(V)(15 pts) Find the exact slope of the tangent line to the polar curve r = 5+ cos(28) at the point corresponding to B = 7/6. (VI)(20 pts) Find the exact area of the region that lies inside the polar curve r = 1 + 2 cose and outside the circle r = 2.
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...
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...
(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)).
(a) Find the slope of the tangent line to the graph of the polar curve r = 1 + 2 cos θ at the point where θ = π/3 . (b) What are the x, y coordinates of the point in the curve r = 1 + 2 cos θ where θ = π/4.