MATH 1090 Algebra and Trigonometry
Problem Set 2 - Solutions

2002 Winter

Note

Simplify .

Simplify .

Simplify
To what function of x does this expression tend as h ® 0 ?

As h ® 0, the expression ®

[Note: in MATH 1000 you will see that ; that is, the slope at any point (x, y) on the curve is just .]

Rationalize the numerator of $(sqrt{x} - sqrt{y}) / (x^2 - y^2)$
To what function of x does this expression tend as y ® x ?

[Division by complex numbers (that are neither real nor pure imaginary) is not examinable in 2002 Winter.]
Evaluate and express the result in the standard form (a + bi).

Evaluate and express the result in standard form.

Graph the equation y = x - x^3

y = x - x^3

by plotting points at
x = -2, -3/2, -1, -1/2, 0, 1/2, 3/2, 2

x = -2, -3/2, -1, -1/2, 0, 1/2, 3/2, 2

.

x	x³	y = x - x³
-2.0	-8.000	+6.000
-1.5	-3.375	+1.875
-1.0	-1.000	0.000
-0.5	-0.125	-0.375
0.0	0.000	0.000
+0.5	+0.125	+3.750
+1.0	+1.000	0.000
+1.5	+3.375	-1.875
+2.0	+8.000	-6.000

[Graph of y = x - x^3]

Find the axis intercepts.
The x-axis intercepts are at .
The y-axis intercept is at only.

Find the distance between the points (-2, 6) and (1, 0).
Find the midpoint of the line segment joining the points (-2, 6) and (1, 0)
The midpoint is at .

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Dr. G.H. George