#2. Use a graphing utility to determine which of the given viewing rectangles produces the most appropriate graph of the function .	Given Problem.
We know the plot command, so we enter: plot({sqrt(8*x-x^2), x=-10..10);	The result looks like this:
We should know from algebra that if we square both sides of the original problem we get:	We can see here that we really have the top half of a circle whose center is located at (4,0), and whose radius is 4.
Now we realize what we really have, and can intelligently choose our domain: plot({sqrt(8*x-x^2), x=-2..10);	Now our result looks like this:
This still doesn't look like a semicircle. Here Maple has automatically picked a range for us which distorts our curve. So we now pick a range also: plot({sqrt(8*x-x^2)}, x=-2..10, y=-6..6);	Now our result looks like this:
If we want to see the other part of the circle (which is not a part of the function in the problem), then we could enter: plot({sqrt(8*x-x^2),-sqrt(8*x-x^2)}, x=-2..10, y=-6..6);	This would then be the result:

1.4, #20. (a) Use a graph to show that the equation  has exactly three solutions.
 

Two curves are equal when they coincide or intersect. Graph each of the equal functions in the problem.
In Maple, this can be done by using the following multiple plot command: >plot([cos(x),.3*x],x=-5..2);
We can clearly see that there are three intersection points	Therefore, we have shown that there are three solutions.

1.4, #20 (b). Find an approximate value of m such that the equation has exactly two solutions.
 
 

Two curves are equal when they coincide or intersect. Graph each of the equal functions in the problem, trying different values for m.
Using the multiple plot command in Maple, this can be done by literally trying a number of coefficients for x and plotting them, observing which ones get close to intersecting the "hump" of the cosine curve in only one point. Thus, we will have 2 solutions. >plot([cos(x),.3*x,.4*x,.34*x],x=-5..2);
It also seems reasonable that this could also happen if the slope to our line was negative. So I tried... >plot([cos(x),-.34*x],x=-5..4);
It appears that both of these values for m, namely +.34 and -.34 yield 2 solutions.

	Assignment
15, 21, 23, 25, 27, 29
Lesson 1.4, Pages 55-56