P R E CALCULUS
1
REVIEW
1.1 Real Numbers, Functions, and Graphs
Preliminary Questions
1. Give an example of numbers a and b such that a < b and |a| > |b|.
SOLUTION
Take a = 3 and b = 1. Then a < b but |a| = 3 > 1 = |b|.
2. Which numbers satisfy |a| = a? W
5 THE INTEGRAL
5.1 Approximating and Computing Area
Preliminary Questions
1. Suppose that [2, 5] is divided into six subintervals. What are the right and left endpoints of the subintervals?
If the interval [2, 5] is divided into six subintervals, the leng
APPLICAT IONS OF
4
THE DERIVAT IVE
4.1 Linear Approximation and Applications
Preliminary Questions
1. Estimate g(1.2) g(1) if g (1) = 4.
SOLUTION
Using the Linear Approximation,
g(1.2) g(1) g (1)(1.2 1) = 4(0.2) = 0.8.
2. Estimate f (2.1), assuming that f
3 DIFFERENTIATION
3.1 Definition of the Derivative
Preliminary Questions
1. Which of the lines in Figure 10 are tangent to the curve?
D
B
C
A
FIGURE 10
SOLUTION
Lines A and D are tangent to the curve.
2. What are the two ways of writing the difference quo
2 LIMITS
2.1 Limits, Rates of Change, and Tangent Lines
Preliminary Questions
1. Average velocity is defined as a ratio of which two quantities?
SOLUTION
Average velocity is defined as the ratio of distance traveled to time elapsed.
2. Average velocity is