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Answers to Exercises; Chapter 4 303

When x < -2,

0 < 4x2(2x2 - 1) < 8x4 - 4x2 - 3x + 3 < (3x2 - I)~;

when -2 < x < 1,

0 <(3x2 - 1)2 < 8x4 - 4x2 - 3x + 3;

when 1 < x,

0 < x2+3=8x2 -4x2-3x2+3 <8x4 -4x2 -3x+3 <(3x2 - 1)2.

From these inequalities follow the desired conclusions.

(c) tan0 = a- 1; tan28 = 3-2fi; tan38 = fi+ 1; tan238 =

3 + 2fi. The asymptotes of (C) are the straight lines y2 = (3 f 2fi)x2 or

y = f(tan 0)x, y = f(tan 30)x. Note that the locus of (D) is the union of

the loci y = 0 and y2 = x2 - 1 + (3/4x); its asymptotes are the straight

lines y = 0, x = 0 and y = fx.

(4

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5.1. (b)