
1. Given the polar curve: r = 2coso, OSO < 21 : a) Name the shape...
3 TT Find the slope of the tangent line to polar curve r = 7 – 6 sin 0 at the point ( 7 – 6- 2 2 3 TT TT Find the points (x, y) at which the polar curve r = 1 + sin(e), 0 < has a vertical 4 4. and horizontal tangent line. Vertical Tangent Line: Horizontal Tangent Line:
(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)).
Find the points of horizontal tangency to the polar curve. r = a sin ose<, a > 0 (r, 0) = (smaller r value) (r, 0) = (larger r value) Find the points of vertical tangency to the polar curve. (r, ) = (smaller e value) (r. 2) = (larger e value)
2. Carefully sketch the curve whose polar equation is r -7 cos(6). Include work that shows how you drew the graph. 3. Carefully sketch the curve whose polar equation is r 2+sin . Include work that shows how you drew the graph.
2. Carefully sketch the curve whose polar equation is r -7 cos(6). Include work that shows how you drew the graph. 3. Carefully sketch the curve whose polar equation is r 2+sin . Include work that shows how...
Plot the point given in polar coordinates and find three additional polar representation of the point, using –211 << 21. (Copy the polar coordinate below to a sheet of paper and then graph the points. Label your points). (3 pts) Representations (Other three) A) (4,5) (3 pts) B) (-3, ---) 90° 4 120° 60° 3 150° 2 30° 180° 0° 210° 330° 240° 300° 2700
Given: r(t) = <t, <t,>, a) sketch the plane curve represented byř (indicate the orientation), b) find the velocity, acceleration and speed functions, c) find the values of t for which the speed is increasing, d) find and sketch the vectors: ř(1), 7(1), and ā(l), (on your graph), and e) find ī (1) and N(1).
just make circle questions which 2,(b) and 3,(i) thank
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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...
2. a) Show that the (signed) curvature for a curve in polar coordinates (r, 0) is given by where ro denotes do Hint: derive the formulas r-r(0)cosa, y-r(θ)sin θ with respect to θ b) Compute the signed curvature for the cardioid r(0) 1-sin θ Sketch the curve with a suitable plotting tool.
2. a) Show that the (signed) curvature for a curve in polar coordinates (r, 0) is given by where ro denotes do Hint: derive the formulas r-r(0)cosa, y-r(θ)sin...
NAME Q2. (24pts) Consider the eurve given in polar coordinates by 11 sin(0)Veos(). (-/ 2 < e</2) . r 6) Make a table of the values of the function f()- 11 sin(0) /co0) -Se/12)-/3-/4 6-/12 /12 | /6 /4 /3 | 5/12 -/2 tatwatwlaat on 1-r/2./2: all the values f(0) are to be rounded to two decimal places, (Hint. Ciaen an angle 0, enter the value of to the variable C of your caleulator, and then evaluate f(e) using the...
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...