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MAT284-2007Spring

MAT284-2007Spring - x>3 x 2:3 5(12 points Use the...

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Math 284, Final Exam (Spring 2007) Student Name: Student Number: Lecture Class Instructor Name (check one): Datta, Gogus, Xu Recitation Class Instructor Name: Problem 1: Problem 2: Problem 3: Problem 4: Problem 5: Problem 6: Problem 7: Problem 8: Problem 9: Problem 10: Total: 1

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1. (a) (5 points) Find an equation of the line passing through the point (-2, 6) and perpendicular to the line 3y + 8x = 4. (b) (5 points) Rewrite the equation you found in part (a) as a general linear equation. (c) (5 points) Find the x-intercept and y-intercept of the equation you found in part (a). x-intercept = y-intercept = 2. (10 points) Find the equilibrium point if the supply and demand equations are p = 2q + 10 and p = 20 - q, respectively. 2
2 3. (a) (5 points) Find x, if logx(6 + 4x - x ) = 2. (b) (5 points) Find x, if g2x+l = 3. 4. Find the limits: (a) (5 points) limt--42 t2~5;+6 3

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(c) (5 points) lim

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Unformatted text preview: x-->3 x 2 ::3 5. (12 points) Use the definition of the derivative to find j'(x) if f(x) = x 2 + x. 4 4 6. (11 points) Find an equation of the tangent line to the curve y = x-2x: 3 + 3x - 4 when x=1. 7. Find the derivative y' of the following functions: (a) (5 points) y = 2 2 " (b) (5 points) y = log2(x 2 + 1) (c) (5 points) y = (~~=~t 5 4 8. Let f(x) = x-2x 2 + 4 be the given function. (a) (5 points) Find the intervals where the function f is decreasing or increasing. (b) (5 points) Find the intervals where the function f is concave up or concave down. (c) (5 points) Find relative maxima and minima of f. 9. Find the indefinite integrals for the following functions: 4dx (a) (5 points) .r x 6 (b) (5 points) J3e xdx 10. (12 points) If the marginal-revenue function for a manufacturer's product is dr 2- = 2001 - lOq -3q dq find the demand function. 7...
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MAT284-2007Spring - x>3 x 2:3 5(12 points Use the...

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