16 - MAT 140 Differential Calculus w/Review Old Midterm...

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Unformatted text preview: MAT 140: Differential Calculus w/Review Old Midterm Exam # 1 1. (a) Specify the equation of a line perpendicular to the line passing through the points (0, 2) and (5, −1). (b) Specify a sequence of graphs, beginning with a basic function and ending with the function: 4 − (x + 2)2 . 2. For each of the following relations,: • specify if the relation is a function or not, • if a function, specify the domain of f (x) and the value of f (2). (a) (b) (c) (d) (e) (f) { (0, 1), (2, 1), (0, 2), (3, 3), (1, 6) } { (0, 2), (2, 2), (−2, 6), (4, 6), (8, 2) } { (x, y ) | x = y 2 } √ { (x, y ) | y = x } f (x) = f (x) = 4x x+2 2x + 1 3x x < −2 x > −3 x<1 x>3 3. Working with the given graph: (a) Explain why the graph represents a function. (b) Specify the intervals on which the function is: i. positive ii. decreasing iii. concave down (c) Identify any points of inflection. (d) Identify any maximum values for the function - classify the maximum as local or global. 4. (a) Specify the average rate of change for f (x) = x3 + 1 from x = 0 to x = 2. (b) Specify the average rate of change for f (x) = 3x + 1 from x = 0 to x = 2. 5. Discuss the continuity of: f (x) = x2 + 1 x−1 x−2 x<1 x≥1 6. Express | x2 − 3x | as a piecewise function. √ x 7. Given: f (x) = x2 + 1 g (x) = (x + 2)3 h(x) = specify the following: (a) h ◦ f (x) = (b) h ◦ g ◦ f (x) = 8. Specify the value of the following: (a) (b) x2 − 9 x→3 x2 − 5x + 6 lim x2 − 4 x→2 x2 + x − 6 lim 9. (a) Define lim f (x) = L. x→c (b) Discuss the relationship between lim f (x) and f (c). x→c 10. Complete the chart: c 1 2 3 4 5 7 f (c) limx→c f (x) limx→c f (x) limx→c f (x) 11. Answer the following questions about the function: x2 − 1 x<0 x+3 x2 0<x<2 f (x) = (x+2)(x−2) 2<x x− 2 (a) (b) (c) x→−3 − x→0 − x→2 − lim f (x) = x→−3 + x→0 + x→2 + lim f (x) = lim f (x) = lim f (x) = lim f (x) = lim f (x) = ...
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16 - MAT 140 Differential Calculus w/Review Old Midterm...

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