b. How many of these students were infected after four days? c. When will 200 of these students be infected? d. What is the maximum number of students that will be infected? Evaluate. 18. 1 3 cos 2 Sin 19. tan sec 3 Arc x 20. Convert 2 6 cos 0 r r into rectangular form. 21. Sketch the graph of 2 2sin r . 22. Sketch the graph of 1 2cos r .
Calculus Maximus Limits Page 3 of 4 Find the limit. 23. 3 3 3 lim 27 x x x 24. 0 2 2 lim y y y 25. 2 3 3 3 4 lim 5 2 x x x x x Use the power rule to find the derivative when needed. 26. Find the slope of the line tangent to 3 2 ( ) 3 4 f x x x x at the point 1,2 . 27. Find an equation of a line that is tangent to 2 ( ) 5 g x x and is perpendicular to the line 6 7 0 x y Use the limit definition of the derivative to find the derivative of each function. 28. 2 ( ) 1 f x x 29. ( ) 2 1 f x x
Calculus Maximus Limits Page 4 of 4 Write a function, and use your graphing calculator to solve. Give decimal answers correct to three decimal places. 30. A container with a square base, vertical sides, and an open top is to be made from 1000 2 ft of material (assume no waste.) Find the dimensions of the container with greatest volume. 31. A piece of wire 10 m long is cut into two pieces. One piece is bent into a square, and the other is bent into an equilateral triangle. How should the wire be cut so that the total area enclosed is a. A maximum? b. A minimum? 32. On the same side of a straight river are two towns, and the townspeople want to build a pumping station at point S . Find the distance from S to Town 1 that will minimize the total length of pipe.
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