Download PDF by Robert Carl Yates: Analytic geometry with calculus

By Robert Carl Yates

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4. 010101 . 123123123 5. Show that sin B - B (a) Limit 0--+ 0 0 =0 (b) Limit 0-0 1 - cos B 02 = 6. Using a table of sines and cosines, draw in rectangular coordinates the graphs of (a) y = 2 sin x (b) y = sin 2x (c) y = sin (x/2) (d) y = 1- cos x. 7. Draw and discuss the graph of (a) y= (b) y x2 - 4 x- 2 (= x + 2, x 0 2). x2-5x+6 (= x - 2, z 0 3). x- 3 8. Draw the region defined by (a) {r = sin B, r S cos 01 (b) {r < sin B, r sin 9 9. Draw(( the graph of (a) 1r sin6+rcos06 4,050= (b) rr= 1,-6595 341 1 34 } Sec.

Explicitly, 4 y = x- 1' x 0 1, which for all real numbers, except x = 1, gives numbers y. Thus, assured that y is indeed a function of x, x 0 1, we apply the delta process to the Sec. 1 THE DERIVATIVE 46 original equation. Thus (x+Ax)(y+Ay) - (y+Dy) -4=0, (1) or xy + x(Ay) + y(Ax) + (Ax) (Ay) - y - (Ay) - 4 = 0. x(Ay) + y(Ax) + (Ox) (Ay) - (Ay) = 0 (2) oy x-+y+ (oy) O:r (3) 1 1 Ay Ax =0 1 1 (4) Thus x x0 1. EXERCISES Using the delta process, find Dry: 1. xy + x2 = 1 2. xy- x2= 1 3. xy2-4=0 5. y = 7.

010101 . 123123123 5. Show that sin B - B (a) Limit 0--+ 0 0 =0 (b) Limit 0-0 1 - cos B 02 = 6. Using a table of sines and cosines, draw in rectangular coordinates the graphs of (a) y = 2 sin x (b) y = sin 2x (c) y = sin (x/2) (d) y = 1- cos x. 7. Draw and discuss the graph of (a) y= (b) y x2 - 4 x- 2 (= x + 2, x 0 2). x2-5x+6 (= x - 2, z 0 3). x- 3 8. Draw the region defined by (a) {r = sin B, r S cos 01 (b) {r < sin B, r sin 9 9. Draw(( the graph of (a) 1r sin6+rcos06 4,050= (b) rr= 1,-6595 341 1 34 } Sec.

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Analytic geometry with calculus by Robert Carl Yates


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