Pre-Calc Homework Solutions 454

Pre-Calc Homework Solutions 454 - 454 Appendix A3 11. (a)...

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Unformatted text preview: 454 Appendix A3 11. (a) lim (sin x) x1 7. Step 1: 19 x 3 1 1 19 x 3 1 19 x 4 4 19 x 16 2 4 x 19 16 15 x 3 or 3 x 15 Step 2: x 10 x 10 10 x 10. Then 10 3 7, or 10 15 5; thus 5. sin 1 sin 1 0.01 0.841 0.01 sin 1 sin x 0.01) 1 (b) Step 1: sin x sin x 0.01 0.01 sin 1 x 0.01 sin 1 sin 1 (sin 1 sin 8. Step 1: x 2 4 0.5 0.5 x 2 4 0.5 2 3.5 x 4.5 3.5 x 4.5 4.5 x 3.5, for x near 2. Step 2: x ( 2) x 2 2 x 2. Then 2 4.5 4.5 2 0.1213, or 2 3.5 2 3.5 0.1292; thus 4.5 2 0.121. 9. (a) lim x 5 (sin 1 x 1 . 1 0.01) 1 Step 2: x 1 1 x Then 1 1 Choose Alternately, graph y1 1 sin sin 1 sin sin 1 1 (sin 1 0.01) 0.01) 0.0182, or (sin 1 (sin 1 0.01) 0.01) 1 0.0188. (sin 1 x 2 6x 5 x 5 lim x 5 (x 5)(x 1) x 5 lim (x x 5 1) 0.018. sin x, y2 sin 1 1, and 4, x (b) Step 1: x2 5. 6x 5 x 5 ( 4) (x 0.05 4 0.05 5 5. 5 y3 x x sin 1 0.98175 1.01878 0.018. 1. The curve intersects the lines at 1 1 0.01825 and at 0.01878. We may choose Step 2: x Then 0.05 4.05 5.05 ( 5) 5 5)(x 1) x 5 x x 1 3.95, x 4.95, x x 5 4.95 2x) 4) 2x) 2 2 x 5. 5.05 0.05, or 0.05. [0.9, 1.1] by [0.78, 0.88] 5 10. (a) lim f (x) x1 0.05; thus 2 and 2, so lim f (x) x1 lim (4 x1 lim f (x) x1 lim (6x x1 2. 2x 0.5 (b) Step 1: x 1: (4 x 2 0.5 0.5 2 3 ; 4 x 1: (6x x 4) 6 6 2 0.5 0.5 6x 13 . 12 6 0.5 Step 2: x 1 Then 1 1 x 3 4 x 1 . 1 1 . Choose 12 1 , or 1 4 1 . 12 13 12 ...
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