UUIILS Sdve (6pts) Find the length of the polar curve =4-2 COS O an tl on the interval O E[0,1]. "(may use calculator to integrate) TT TT Paragraph 4 Arial 3 (12pt) : - E - T- III
(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)).
1. Given the polar curve: r = 2coso, OSO < 21 : a) Name the shape and sketch the graph: m2 21/3 TT/3 511/B 1/6 TT 0 711/6 11T/6 411/3 5/3 31/2 I c) Determine where the curve has horizontal tangents.
(1 point) A curve with polar equation r = 27 8 sin 0 + 49 cos 0 represents a line. This line has a Cartesian equation of the form y = mx +b ,where m and b are constants. Give the formula for y in terms of x. For example, if the line had equation y = 2x + 3 then the answer would be 2 *x+3. Hint: multiply both sides by the denominator on the right hand side and...
Directions: In 1-6, determine the polar form of the given rectangular equation. [1] 36x² + 36y² = 3600 A. = 360° B. r= 100 C. r=-10 D. r = 36 E. none of these [2] 16x - 5y = 20 A r = 16 -5cos + 20 sine B. r = -5 20cos + 16 sin c. r = 20 16 cos 0 - 5sine D. = tan 16 5 272.646° E. none of these [3] y = x A....
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:
s(100) 10.Find the area enclosed by the polar curve r = 5 cos 10 12.57T 257T 11. Determine whether the series is convergent or divergent by expressing it as a its sum telescoping sum. If it is convergent, find 00 In n+1 n=1 1 O In 2 -1 O The series is divergent. 12. Use the Comparison Test or the Limit Comparison Test to determine if the following series converges or diverges. 3 5 n=1 n5+5 converges diverges s(100) 10.Find...
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.
ingedit (-Scoscan) sex = 7 Select one: TT a. wla TT 3 cos(f)dt 0 O b. Z TT 2 cos(t)dt 21 C. 3 cos(t)dt TT d. 3 л 2 Sv2 cos(?)dt
Consider the following Polar Graphs: Figure 1 is below: Figure 2 is below: Polar Axis b* Polar Axis Figure 3 is below: Figure 4 is below: If ifik 1001kle Polar Axis Polar Axis Figure 5 is below: Figure 6 is below: Polar Axis Polar Axis Figure 7 is below: Figure 8 is below: Polar Polar Axis | Ε Figure 9 is below: Figure 10 is below: 18181% a d Polar Axis" Polar Axis Figure 11 is below: Figure 12 is...