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# Homework1 - 1 2.7.46 a Rate of bacterias/hour after 5 houts...

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1. Section 2.6: Limits at Infinity; Horizontal Asymptotes 2.6.4. a) 2 b) 2 c) 1 d) 1 e) 1 f) Horizontal asymptotes: y = 2, y = 2; Vertical asymptotes: x = 2, x = 0, x = 3 2.6.22. 1 3 (factor out x from the numerator and pull out the x 2 from inside the square root) 2.6.32. 1 (factor out x 3 from the numerator and x 2 from the denominator) 2.6.34. tan 1 ( 1) = 2 (by continuity of tan 1 ) 2.657.5 (by the squeeze theorem) 2. Section 2.7: Derivatives and Rates of Change 2.76.y = x + 4 ((y 3) = (x + 1) is also acceptable) 2.7.12. a) A runs with constant speed, while B is slow at rst and then speeds up b) 8.5 seconds c) 9 seconds 2.7.17.g 0 (0) < 0 < g 0 (4) < g 0 (2) < g 0 ( 2) 2.7.18. a) y = 4x 23 (y + 3 = 4(x 5) is also acceptable) b) f(4) = 3, f 0 (4) = 1 4 p 2.7.32. f(x) = 4 x, a = 16 2.7.34. f(x) = tan(x), a = 4 2.7.40. 5 6 F/min (slope of the red line)

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Unformatted text preview: 1 2.7.46. a) Rate of bacterias/hour after 5 houts b) f (10) > f (5) (basically, the more bacteria there are, the more can be produced). But if there's a limited supply of food, we get that f (10) < f (5), i.e. bacterias are dying out because of the limited supply 3. Section 2.8: The derivative as a function 2.8.3. a) II b) IV c) I d) III 2.8.21.f (t) = 5 18t 2.8.38. 1 (not continuous there); 2 (graph has a kink) 2.8.43. a) Acceleration b) Velocity c) Position 2.8.52.Not di erentiable at the integers, because not continuous there; f (x) = 0 for x not an integer, unde ned otherwise. Graph looks like the 0-function, except it has holes at the integers....
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Homework1 - 1 2.7.46 a Rate of bacterias/hour after 5 houts...

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