[1] 1. (a) Solve 2 – 31 < 7.
Solution: We have – 7<-3 < 7 which gives -4 0 on (-0, 1] U [2,).
Next, we need to see where Vr2 – 3r +2 -1 > 0. If r2 - 3.c + 2 – 1 > 0, then
V.22 – 3.0 +2 > . Observe that this is definitely true if r < 0. If r > 0, then squar-
ing both sides we get
22 - 3.+2 > 1
2 > 3.
V
A
VICO
Thus, the domain of f is (-00, ).
[2] (c) Find the exact value of tan(sec-14).
Solution: Let y = sec-14. Then, sec y = 4. From the diagram we get that
tan(sec-? 4) = tan y = 15
[2] (d) Find all r such that sin(2.x) = COS I.
Solution: We have 2 sin r cos r = COS I, SO 0 = 2 sin Cos I -Cos I = cos .r (2 sin c - 1).
Hence, sin(2x) = cost when cos x = 0, or when sin r = Thus,
r=
+ik, kez, I=
+2nk, ke Z, or r=
+2nk, kez
[2] (e) State the precise mathematical definition of lim f(x) = 0.
Solution: For every e > 0 there exists a 8 >0 such that if 0 < x-al <, then f(c) >
