please show work and explain each part clearly 9. The curve given by its equation in...
The curve shown below is called a Bowditch curve or Lissajous figure. Find the point in the interior of the first to the curve is horizontal, and ind the equations of the two tangents at the origin. What is the point in the interior of the frst quadrant where the tangent to the curve is horizonta? an ordered pair. Type an exact answer, using radicals as needed ) What is the equation of the tangent at the origin when t...
please explain how you do part (b) clearly. Given the curve x-t5, y--t+4t +3, find the exact values: 18) a) of the coordinates of the leftmost point on the curve. (Use Calculus and show your work). b) of the parameter t where the graph crosses itself. (Use any method you wish - but show your work). c) of the parameter t where the slope of tangent line to the curve is(Use Calculus and show your work).
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...
(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...
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
number 1and2 Turn in the following problems at the start of your Thursday recitation section To receive full credit, please staple your work, and put your name, your section number, and the homework number at the top. 1. (a) Find a Cartesian equation for the polar curve 3 sin 4 +4cos 6. (b) Use the Cartesian equation you found in part (a) to graph the curve. What is its geometric shape? 2 Carefully sketch the curve wheose polar equation isr...
please answer the question and show all your work thank you ? Then graph it. 5) (15 points) a) Sketch the graph of the curve r = 1 + sin 8 for 0 SO S2 b) Find the slope of the tangent line to this curve at 0 = c) Find the polar coordinates of the points on this curve where the tangent line is horizontal
(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.
The region inside the curve r= 4 cos θ and outside the curve r = 2. r(t) 2 rt)4cos(t) -1 What are the coordinates of the point where the two circles intersect at the top of the picture in terms of (r,0) What are the coordinates of the same point in cartesians coordinates (x.y)? Give an equivalent version of the point in polar coordinates with r <o. What is the slope of of the tangent line to the circler 2...