Page 64 - Calculus Demystified

CHAPTER 1
b c
;
(b) (a ) = a b·c Basics 51
a b
(c) a b−c = .
a c
These are really just restatements of properties of the logarithm function that we
have already considered.
4
4
3
2
3
You Try It: Simplify the expressions 3 · 5 /(15) and 2 · 6 · 12 −4 .
Exercises

1. Each of the following is a rational number. Write it as the quotient of two
integers.
(a) 2/3 − 7/8
(b) 43.219445
−37 −4
(c) ·
533 −6
2
(d)
3.45969696 ...
(e) −73.235677677677 ...
3
(f) 5
−17 + 3
4 9
−4 + 2
(g) 9 5
−11 + 6
3 7
(h) 3.2147569569569 ...
√ √
2. Plot the numbers 3.4, −π/2, 2π, − 2 + 1, 3 · 4, 9/2, −29/10 on a real
number line. Label each plotted point.
3. Sketch each of the following sets on a separate real number line.
(a) S ={x ∈ R:|x − 2| < 4}
2
(b) T ={t ∈ R: t + 1 = 5}
(c) U ={s ∈ R: 2s − 5 ≤ 3}
(d) V ={y ∈ R:|6y + 1| > 2}
2
(e) S ={x ∈ R: x + 3 < 6}
(f) T ={s ∈ R:|s|=|s + 1|}