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(Parte 1 de 4)

CHAPTER 4

Exponential, Logarithmic, and Inverse Trigonometric Functions

EXERCISE SET 4.1

2. (a) They are inverse functions. 2

(b) The graphs are not reﬂections of each other

(c) They are inverse functions provided the domain of

(d) They are inverse functions provided the domain of f(x)

3. (a) yes; all outputs (the elements of row two) are distinct (b) no; f(1) = f(6)

Exercise Set 4.1 123

4. (a) no; it is easy to conceive of, say, 8 people in line at two diﬀerent times (b) no; perhaps your weight remains constant for more than a year

(c) yes, since the function is increasing, in the sense that the greater the volume, the greater the weight

5. (a) yes (b) yes (c) no (d) yes (e) no (f) no

6. (a) no, the horizontal line test fails 6

(b) yes, horizontal line test 10

7. (a) no, the horizontal line test fails (b) no, the horizontal line test fails (c) yes, horizontal line test

8. (d) no, the horizontal line test fails (e) no, the horizontal line test fails (f) yes, horizontal line test

(b) how many degrees Celsius given the Fahrenheit temperature

(c) how many meters in y miles

Exercise Set 4.1 125

(b) x

(c) no, because f(g(x)) = x for every x in the domain of g is not satisﬁed (the domain of g is x ≥ 0)

(b) symmetric about the line y = x

value of k.

dx , dy

dx , dy

Exercise Set 4.2 127 EXERCISE SET 4.2

original equation) ln3

(b) y

(b) y x

36. (a) y x

Exercise Set 4.2 129 38. 10

40. (a) Let X =log b x and Y =log a x. Then bX = x and aY = x so aY = bX,o r aY/X = b, which means loga b = Y/X. Substituting for Y and X yields loga x logb x =log a b,logb x = loga x loga b

42. Since the units are billions, one trillion is 1,0 units. Solve 10 =0 .051517(1.1306727)x for x by taking common logarithms, resulting in 3 =log 0.051517 + xlog1.1306727, which yields x ≈ 7.4, so the debt ﬁrst reached one trillion dollars around 1977.

43. (a) no, the curve passes through the origin (b) y =2 x/4

4. (a) As x → +∞ the function grows very slowly, but it is always increasing and tends to +∞.A s x → 1+ the function tends to −∞.

(b)

46. Let x =log b a and y =log b c,s o a = bx and c = by.

51. (a) 140 dB; damage (b) 120 dB; damage (c) 80 dB; no damage (d) 75 dB; no damage

54. The decibel level of the nth echo is 120(2/3)n;

EXERCISE SET 4.3

= 2lnx sinx (cosx) =cot x

Exercise Set 4.3 131

lnx lnxx√ 1+l n2 x

23. dy

24. ex cos(ex)

31. dy x dy

32. dy xtany xsec2 y dy dx = tany

dx = dx =

y = πsinx,l ny =(sin x)lnπ, 1 y y′ =(ln π)cosx, y′ = πsinx(lnπ)cosx y = πxtanx,l ny =( xtanx)lnπ, 1

Exercise Set 4.3 133

(Parte 1 de 4)