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t1 - ∞ 2 x 1 x 1(c lim w-→ x 2-4 w(d lim s-→ 6 s 2-3...

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Methods of Calculus MAC3233 Test 1 September 19, 1990 (1) (20 points) Consider the graph displayed in Figure 1. Answer the following questions. (a) Is the function continuous at the point where x = a ? (b) Is the function differentiable at the point d ? (c) Is the function continuous at the point d ? (d) Is the function differentiable at the point where x = f ? (e) Is the function differentiable at the point where x = b ? (2) (20 pts.) Differentiate the following. (3) f ( x ) = 2 x (4) g ( x ) = 1 x 2 + x + 1 (5) y = (2 x 2 - x + 4) 6 (6) s ( t ) = 2 - 2 t 3 (7) (10 pts. ) Use limits to compute f 0 (3), where f ( x ) = x 2 + 1. (8) (20 pts.) Evaluate the following limits. (a) lim x -→ 1 x 2 - 1 x - 1 (b) lim x -→
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Unformatted text preview: ∞ 2 x + 1 x + 1 (c) lim w-→ x 2-4 w (d) lim s-→ 6 ( s 2-3 s + 5) (9) (10 points) Determine the equation of the tangent line to the curve y = x 3 + 3 x-8 at the point where x = 2. (10) (5 pts.) Evaluate d 2 dt 2 ( t 1 00 + t + 1 ) . (11) (15 points) Flu is spreading through a small school. At time t days after the beginning of the epidemic, there are P ( t ) students sick, where P ( t ) = 20 t-t 2 . (a) At what rate is the flu spreading when t = 1? (b) How many students are sick when the flu is spreading at the rate of 8 students per day? 1...
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