By Edmond C. Tomastik
CALCULUS: purposes AND know-how is a contemporary textual content that's guided via 4 simple rules: the rule of thumb of 4, expertise, the way in which of Archimedes, and an exploratory instructing process. the place acceptable, each one subject is gifted graphically, numerically, algebraically, and verbally, assisting scholars achieve a richer, deeper realizing of the cloth. A suggested emphasis within the textual content on know-how, even if graphing calculators or pcs, allows teachers to spend extra time educating techniques. also, functions play a primary position within the textual content and are woven into the improvement of the fabric. greater than 500 referenced workouts and countless numbers of knowledge units inside the textual content make this article important and useful for college students. most significantly, this article shall we scholars examine and discover calculus on their lonesome, and realize recommendations for themselves.
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Extra info for Calculus: Applications and Technology, 3rd Edition
Revenue is the price of each unit times the number of units sold. Let x denote the number of units of a given product or commodity produced by a firm. ) The units could be bales of cotton, tons of fertilizer, or number of automobiles. In the linear cost model we assume that the cost m of manufacturing one unit is the same no matter how many units are produced. Thus, the variable cost is the number of units produced times the cost of each unit: variable cost = (cost per unit) × (number of units produced) = mx If b is the fixed cost and C(x) is the cost, then we have the following: C(x) = cost = (variable cost) + (fixed cost) = mx + b CONNECTION What Are Revenues?
To find the break-even quantity, set P (x) = 0 and solve for x. , for profits to be zero). Remark Since P = 0 if and only if R = C, we could have found the break-even quantity in Example 2 by setting R = C, obtaining 4800x = 3840x + 300,000. Then solve for x. 2 Mathematical Models 31 Exploration 1 Finding the Break-Even Quantity Graphically Find the approximate break-even quantity in Example 2 on your graphing calculator or computer by finding where P = 0 and also by finding where C = R. In 1997 Fuller and coworkers25 at TexasA& M University estimated the operating costs of cotton gin plants of various sizes.
F (x) = x 2 + 4 √ √ 62. f (x) = x 2 − 9 61. f (x) = 9 − x 2 √ x 63. f (x) = x−5 √ 1 − x , x ≤ −2 x+4 64. f (x) = √4 − x, x > −2 1 2 3 4 5 x 66. Find all points where the function given in the following graph is not continuous. y 0 x 65. Find all points where the function given in the following graph is not continuous. Applications and Mathematical Modeling 67. Packaging Abox has a square base with each side of length x and height equal to 3x. Find the volume V as a function of x. 68. Packaging Find the surface area S of the box in Exercise 67 as a function of x.
Calculus: Applications and Technology, 3rd Edition by Edmond C. Tomastik