Chapter 11

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January 27, 2005 11:47

L24-ch11

Sheet number 1 Page number 475

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CHAPTER 11

Analytic Geometry in Calculus EXERCISE SET 11.1 c/ 2

1. (5, 8)

(1, 6 )

(–3, i)

(–5, @)

(3, 3)

(–1, r)

(4, e)

c/ 2

2.

( 32 , L) (0, c)

0 (–6, –p)

(2, g)

0

(2, $)

√ 3. (a) (3 3, 3) (d) (0, 0)

√ (b) (−7/2, 7 3/2) √ (e) (−7 3/2, 7/2)

√ (c) (3 3, 3) (f ) (−5, 0)

√ √ 4. (a) (− 2, − 2) (d) (3, 0)

√ √ (b) (3 2, −3 2) (e) (0, −4)

√ √ (c) (2 2, 2 2) (f ) (0, 0)

5. (a) (5, π), (5, −π) √ √ (d) (8 2, 5π/4), (8 2, −3π/4)

(b) (4, 11π/6), (4, −π/6) (e) (6, 2π/3), (6, −4π/3)

(c) (2, 3π/2), (2, −π/2) √ √ (f ) ( 2, π/4), ( 2, −7π/4)

6. (a) (2, 5π/6)

(c) (2, −7π/6)

(b) (−2, 11π/6)

(d) (−2, −π/6)

7. (a) (5, 0.9273)

(b) (10, −0.92730)

(c) (1.27155, −0.66577)

8. (a) (5, 2.2143)

(b) (3.4482, 2.6260)

(c) ( 4 + π 2 /36, 0.2561)

9. (a) r2 = x2 + y 2 = 4; circle

(b) y = 4; horizontal line

(c) r = 3r cos θ, x + y = 3x, (x − 3/2) + y = 9/4; circle (d) 3r cos θ + 2r sin θ = 6, 3x + 2y = 6; line 2

2

2

2

2

10. (a) r cos θ = 5, x = 5; vertical line (b) r2 = 2r sin θ, x2 + y 2 = 2y, x2 + (y − 1)2 = 1; circle (c) r2 = 4r cos θ + 4r sin θ, x2 + y 2 = 4x + 4y, (x − 2)2 + (y − 2)2 = 8; circle 1 sin θ (d) r = , r cos2 θ = sin θ, r2 cos2 θ = r sin θ, x2 = y; parabola cos θ cos θ √ 11. (a) r cos θ = 3 (b) r = 7 (c) r2 + 6r sin θ = 0, r = −6 sin θ (d) 9(r cos θ)(r sin θ) = 4, 9r2 sin θ cos θ = 4, r2 sin 2θ = 8/9 12. (a) r sin θ = −3 (c) r2 + 4r cos θ = 0, r = −4 cos θ (d) r4 cos2 θ = r2 sin2 θ, r2 = tan2 θ, r = tan θ

475

(b) r =

5


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