Page 66 - Calculus Demystified

Basics
CHAPTER 1
(a) f assigns to each person his biological father 53
(b) g assigns to each man his dog
(c) h assigns to each real number its square root
(d) f assigns to each positive integer its cube
(e) g assigns to each car its driver
(f) h assigns to each toe its foot
(g) f assigns to each rational number the greatest integer that does not
exceed it
(h) g assigns to each integer the next integer
(i) h assigns to each real number its square plus six
11. Graph each of these functions on a separate set of axes. Label your graph.

2
(a) f(x) = 3x − x
x + 2
(b) g(x) =
x
3
(c) h(x) = x − x 2
(d) f(x) = 3x + 2
2
(e) g(x) = x − 2x
√
(f) h(x) = x + 3
12. Calculate each of the following trigonometric quantities.
(a) sin(8π/3)
(b) tan(−5π/6)
(c) sec(7π/4)
(d) csc(13π/4)
(e) cot(−15π/4)
(f) cos(−3π/4)

13. Calculate the left and right sides of the twelve fundamental trigonometric
identities for the values θ = π/3 and ψ =−π/6, thus confirming the
identities for these particular values.
14. Sketch the graphs of each of the following trigonometric functions.
(a) f(x) = sin 2x
(b) g(x) = cos(x + π/2)
(c) h(x) = tan(−x + π)
(d) f(x) = cot(3x + π)
(e) g(x) = sin(x/3)
(f) h(x) = cos(−π +[x/2])
15. Convert each of the following angles from radian measure to degree
measure.