The italicized phrase before each sample problem indicates a similar problem in James Stewart. 2007. Essential Calculus: Early Transcendentals. Thomson Brooks/Cole: Belmont, CA.
Similar to 1.1.18:
1.2 Spherical volumes
A sphere with radius r centimeters has a volume of V(r) = (4/3)*pi*r^3 cubic centimeters. Consider two spherical beach balls, with radii of r+1 and r+2 centimeters. How much greater is the volume of the second ball than that of the first ball.
Similar to 1.2.8:
1.3 Linear relationships
A concert hall manager knows that if he charges x dollars for each ticket for a particular band, then the number of tickets, y, he will sell can be predicted by the equation y = 3000 - 20x.
a. Graph this equation for the range and domain which is meaningful for this problem.
b. Interpret the slope, and y- and x-intercepts in the context of this problem.
Similar to 1.2.56:
1.4 A ship sailing 45 mph west passes 3 miles directly north of a harbor at time t = 0.
a. Write a function of the westward distance d (in miles) sailed in terms of t.
b. Write a function for the ship's distance s from the harbor in terms of d.
c. Using composition, obtain a function of s in terms of t.
Similar to 1.4.30:
1.7 Suppose for x > 0, 2x - 9 < f(x) < x^2 - 5x + 1. Evaluate limx-->5 f(x).
Similar to 1.4.40:
1.8 Suppose f(x) = 2x - ||x||, where ||x|| is the largest integer that is less than or equal to x.
a. Graph f(x).
b. Let n be an arbitrary integer and determine
| i. limx-->n- f(x) | ii. limx-->n+ f(x)
c. For what values of a does limx-->a f(x) exist? Why doesn't this limit exist for other values of a?
Similar to 1.5.32:
1.9 Determine what value(s) of c will make f continuous for all real values of x.
f(x) = 4x^2 - c^2 for x < 2 and f(x) = cx - 19 for x > 2.
Similar to 1.5.38:
1.10 Using the Intermediate Value Theorem, show there is a value for x in the indicated interval that will satisfy the equation.
cuberoot (x) - x = -3, interval: (0, 8)
Similar to 1.6.24:
1.11 Find the limit.
limx-->+infinity [sqrt (x^2 + 5x) - sqrt (x^2 + 3x)]
Similar to 1.6.34:
1.12 Determine the horizontal and vertical asymptotes for the function. Verify your work by using wolfram.com or a graphing calculator to graph the function and estimating the asymptotes from your graph.
f(x) = (2x + 7) / sqrt (9x^2 + 5x - 4)
