HW Supplement: The Fundamental Theorem of Calculus Name Paul a Gonzalez 1. Find the exact area under the curve of f(x)=√x between x=1 and x=5. vbiad ar griber F(x) = 5's — 2 x ½ 2 F(5)-F(1) = 6.787 50+02:00 wod gribasqa tarona 2. Use your graphing calculator to find an estimate for the area in #1, above. Type the function in Y1=, graph the function. Use 2nd CALC 7: S. Input the limits 1 and 5. Write your answer to 4 decimal places below. If your answers in #1 and #2 do not conform, find and correct your error. 3. What is the difference between the following two problems 3a & 3b? What is similar? Which problem uses the Fundamental Theorem of Calculus? YOU Solve each of the problems. 3a. The resale value of industrial printers decreases over a 10-year period. When a machine is x years old, the value is changing at the rate of 220(x-10) dollars per year. By how much does a printer depreciate in 2nd year? hoot sd auoq 000 Dive dana 3b. The resale value of industrial printers decreases over a 10-year period. When a machine is x years old, the value is changing at the rate of 220(x-10) dollars per year. For a printer that is $11,000 new (x=0), how much is it worth after 5 years?

Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it continues on its course indefinitely. Let D(t) denote its distance from Earth after t years of travel. Do you expect that D has a limiting value?

The cost in dollars of making x items is given by the function Cx)=10x+500. a. The fixed cost is determined when zero items are produced. Find the fixed cost for this item. b.What is the cost of making 25 items? c.Suppose the maximum cost allowed is SI500. What are the domain and range of the cost function, C(x) ?