Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 7. A major complaint of professors teaching calculus is that students don't have the appropriate background to work through the calculus course successfully. This text is targeted directly at this underprepared audience. This is a single-variable (2-semester) calculus text that incorporates a conceptual re-introduction to key precalculus ideas throughout the exposition as appropriate. This is the ideal resource for those schools dealing with poorly prepared students or for schools introducing a slower paced, integrated precalculus/calculus course | Representations of Functions 41 31. Two sisters Nina and Lori part on a street corner. Lori saunters due north at a rate of 150 feet per minute and Nina jogs off due east at a rate of 320 feet per minute. Assuming they maintain their speeds and directions express the distance between the sisters as a function of the number of minutes since they parted. 32. Below are graphs of f g h and j .Use the following clues to match the function with its graph. h 0 g 0 h x g x for x 0 h 2 f 2 j 2 j x 2f x for x 0 For Problems 33 through 35 if the interval is written using inequalities write it using interval notation if it is expressed in interval notation rewrite it using inequalities. In all cases indicate the interval on the number line. 33. a -1 x 3 b -2 -1 34. a -7 x -5 b -w w 35. a -1 x b - 3 36. Let f x 2x2 x. a f 3 d f Find the following. b f 2x e fh c f 1 x 37. A right circular cylinder is inscribed in a sphere of radius 5. a Express the volume of the cylinder as a function of its radius . b Express the surface area of the cylinder as a function of its radius . 38. The height of a right circular cone is one third of the diameter of the base. a Express its volume as a function of its height h. b Express its volume as a function of the radius of its base. 42 CHAPTER 1 Functions Are Lurking Everywhere 39. A vitamin capsule is constructed from a cylinder of length x centimeters and radius r centimeters capped on either end by a hemisphere as shown at left. Suppose that the length of the cylinder is equal to three times the diameter of the hemispherical caps. a Express the volume of the vitamin capsule as a function of x. Your strategy should be to begin by expressing the volume as a function of both x and r. b Express the surface area of the vitamin capsule as a function of x . 40. Calibration function for a bucket Consider the bucket drawn below. The bucket walls can be thought of as a slice of a right circular cone as shown on the right. Let C be the calibration .
