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School: Kentucky
Course: Business Calculus
MA 123 - Business Calculus Summer 2007 P. Busse Quiz 1 Solutions 1. (2 pts) An open box is to be constructed from a 30 30 square piece of posterboard by removing a small square from each corner and folding up the aps to form the sides. Express the volume
School: Kentucky
Course: Elementary Calculus And Its Applications
School: Kentucky
Course: Elementary Calculus And Its Applications
School: Kentucky
Course: Elementary Calculus And Its Applications
School: Kentucky
Course: Elementary Calculus And Its Applications
School: Kentucky
Course: Elementary Calculus And Its Applications
School: Kentucky
Course: Elementary Calculus And Its Applications
School: Kentucky
Course: Elementary Calculus And Its Applications
School: Kentucky
Algebra and Geometry Review We will make use of the Pythagorean Theorem repeatedly throughout the semester. We will also occasionally use facts about similar triangles. The following problems preview some of the ways we will use these geometric facts. 1.
School: Kentucky
Exponential and logarithmic functions Supplement: Practice/review problems The collection of problems listed below contains questions taken from previous MA123 exams. [1]. Suppose that f (x) = ln(g(x). Assume that g(5) = 3 and g (5) = 4. Find f (5). (a) 5
School: Kentucky
Formulas for integrals: integrals, antiderivatives, and the Fundamental Theorem of Calculus Chapter 10: Practice/review problems The collection of problems listed below comprises questions taken from previous MA123 exams. x [1]. Let t2 + 3 dt. h(x) = Find
School: Kentucky
Computing some integrals Chapter 9: Practice/review problems The collection of problems listed below comprises questions taken from previous MA123 exams. [1]. Evaluate the sum 3 + 6 + 9 + 12 + + 30 (a) 55 (b) 550 (c) 110 (d) 275 (e) 165 (e) 2544 (e) 67239
School: Kentucky
The Twenty-first Lecture on March 5 4.2 The Simplex Method: Standard Minimization Problems 1. Minimization with <= Constraints The objective function is to be minimization All the variables involved are nonnegative. Each linear constraint may be w
School: Kentucky
Course: Business Calculus
MA 123 - Business Calculus Summer 2007 P. Busse Quiz 1 Solutions 1. (2 pts) An open box is to be constructed from a 30 30 square piece of posterboard by removing a small square from each corner and folding up the aps to form the sides. Express the volume
School: Kentucky
Course: Elementary Calculus And Its Applications
School: Kentucky
Course: Elementary Calculus And Its Applications
School: Kentucky
Course: Elementary Calculus And Its Applications
School: Kentucky
Course: Elementary Calculus And Its Applications
School: Kentucky
Course: Elementary Calculus And Its Applications
School: Kentucky
Course: Business Calculus
MA 123 - Business Calculus Summer 2007 P. Busse Quiz 1 Solutions 1. (2 pts) An open box is to be constructed from a 30" 30" square piece of posterboard by removing a small square from each corner and folding up the flaps to form the sides. Express the vol
School: Kentucky
Summation Notation and Summation Formulas You may nd the summation formulas useful: n n n(n + 1) k= 2 k=1 k2 = k=1 n(n + 1)(2n + 1) 6 1. Write the sum 1 + 4 + 9 + 16 + 25 + + 196 + 225 in summation notation. Then use a summation formula to nd the value of
School: Kentucky
Optimization Word Problems 1. The product of two positive real numbers, x and y, is 24. (a) Find the minimal sum of these two numbers. (b) Find the minimal value of the expression 3x + 2y. 2. Find the point on the curve y = x which is closest to the point
School: Kentucky
Maximum and Minimum Values 1. On the same graph, plot both f (x) = x3 3x 5 and its derivative. What do you notice? (In particular, what appears to be true about f (x) when the derivative is zero? What appears to be true about f (x) when the derivative is
School: Kentucky
Increasing and Decreasing Functions, Concavity 1. Suppose f (x) = (x 1)(x 4)(x 9) = x3 14x2 + 49x 36. (a) Find the intervals on which f (x) is increasing and the intervals on which f (x) is decreasing. (b) Find the intervals on which f (x) is concave up a
School: Kentucky
Using the Fundamental Theorem of Calculus 1. Compute the integrals (a) 9 dt t (b) 5 3 9 dt t 2. Compute the integrals (a) t3 + t2 + t + 1 dt (b) 3 t3 + t2 + t + 1 dt 3 3. Find the derivative F (x) where x F (x) = 0 e5s ds (s2 + 2s + 19) 4. Find the deri
School: Kentucky
Chapter 7 Two types: (1) maximum-minimum problems and (2) related rate problems 7.2 Max-Min Word Problems o Ask you to find the largest or the smallest value a function has on an interval o Steps Read the problem once over quickly Read the problem