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6 Pages

### review3

Course: MATH 11012, Fall 2008
School: Kent State
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Word Count: 703

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11012 MATH Name: Intuitive Calculus Score: KSU /20 Review Assignment III due Friday, May 6, 2005 For each problem completed (with all work), you will receive 1 point (for a possible 10 points). I will randomly choose one problem to grade for a possible 10 additional points. 1. Let C(x) be the cost, in dollars, of manufacturing x widgets. Fill in the table with a mathematical expression and appropriate units...

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11012 MATH Name: Intuitive Calculus Score: KSU /20 Review Assignment III due Friday, May 6, 2005 For each problem completed (with all work), you will receive 1 point (for a possible 10 points). I will randomly choose one problem to grade for a possible 10 additional points. 1. Let C(x) be the cost, in dollars, of manufacturing x widgets. Fill in the table with a mathematical expression and appropriate units corresponding to each description. Description cost of manufacturing 100 widgets cost of manufacturing the 101st widget average rate of change of cost from a production level of 100 widgets to a production level of 101 widgets instantaneous rate of change of cost at a production level of 100 widgets instantaneous rate of change of cost at a production level of 100 widgets (another expression) 2. Let f (x) be a function. Fill in the table with a mathematical expression corresponding to each description. Description y-coordinate of the point on the graph y = f (x) where x = 27 height above the x-axis of the point on the graph y = f (x) where x = 27 slope of the secant line through the points on the graph y = f (x) where x = 27 and where x = 30 slope of the tangent line to the graph y = f (x) at the point where x = 27 slope of the tangent line to the graph y = f (x) at the point where x = 27 (another expression) Mathematical Expression Mathematical Expression Units 1 3. Let T (t) be temperature, in degrees Fahrenheit, at time t. For each scenario, fill in the banks with one of the symbols <, >, =, or ? (if the sign cannot be determined). (a) The temperature held steady at 70 all afternoon. T (t) 0 T (t) 0 T (t) 0 (b) The temperature increased from the low in the 60's at a slow but steady rate. T (t) 0 T (t) 0 T (t) 0 (c) At midnight, the temperature was 0 and it has been falling more and more rapidly ever since. T (t) 0 T (t) 0 T (t) 0 (d) As the sun came out, the temperature increased more and more quickly. T (t) 0 T (t) 0 T (t) 0 (e) The temperature is still falling, although not as rapidly as earlier in the evening. T (t) 0 (t) T 0 T (t) 0 4. Find the absolute extreme values of the function f (x) = 3x 4 - 16x3 + 18x2 on the closed, bounded interval [-1, 4]. You must show all your steps carefully so that I know you are using calculus rather than relying on your grapher. The absolute minimum value of f on [-1, 4] is The absolute maximum value of f on [-1, 4] is which occurs at x = which occurs at x = . . 2 5. A bank offers money market accounts at 2.75% annual interest compounded continuously. (a) Give the formula for the amount F V in the account after t years when P V dollars are invested. (b) How soon will a deposit triple in value? Show your reasoning. Round to the nearest year. 6. A bank offers money market accounts at 5.25% annual interest. Rounded to the nearest cent, what is the present value of \$1,000 ten years from now . . . (a) . . . if interest is compounded continuously? (b) . . . if interest is compounded weekly? (c) . . . if interest is compounded quarterly? 3 7. Evaluate each indefinite integral. Try simplifying the integrand algebraically instead of or in addition to using a substitution. Show all steps. Check your answer by differentiating. (a) e3x 2 - e3x 5 dx Check: (b) x2 + 2 x3 2 dx Check: (c) ln(1 - x) d...

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Kent State - MATH - 11012
Kent State - MATH - 11012
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