- Introduction
- Solving a function or an expression algebraically
- Solving a function or an expression numerically
- Some more strange output
- Systems of Equations
- Exercises

> g := 9*x^2-14; > h:=-x^2; > plot([g,h],x=-2..2); > solve(g=h,x);The plot shows that there are two intersection points and the

> ip:=solve(g=h,x);Since there are two values called , use [ ] to call up the one you want.

> subs(x=ip[1],g); > subs(x=ip[2],h);Therefore the two intersection points are and . This seems like the answer shown on the graph.

> j:=x->2*x^3-15*x^2-2*x+5; > k:=x->-50; > plot([j(x),k(x)],x=-3..8);The graph shows there should be three answers.

> solve(j(x)=k(x),x);AAAAAAAAAAAAAARG! That is some scary output! So instead of using the algebraic

fsolve(j(x)=k(x),x);

> f:=theta->-1/2*theta+sin(theta); > plot(f(theta),theta=-8*Pi..8*Pi); > solve(f(theta)=0,theta);Wow, what is that?!?! We know from the graph that there should be three answers and

> fsolve(f(theta)=0,theta);Where are the other two answers!? This is actually how

> a:=fsolve(f(theta)=0,theta=-5..-1); > b:=fsolve(f(theta)=0,theta=-1..1); > c:=fsolve(f(theta)=0,theta=1..5);To find the values just plug in the names of the values.

> f(a); > f(b); > f(c);(Of course the y-values are zero!)

>pl1:=7*x+y;pl2:=1-2*x+y/3; >plot3d({pl1,pl2},x=-2..2,y=-2..2,axes=normal,style=[patchnogrid,wireframe], color=["Magenta","Chartreuse"]); >li:=solve({pl1=z,pl2=z});Notice that the solution can be written in parametric form: or it may be written symmetrtically as: .Note that you can do the algebra for the symmetric form with Maple:

> solve(li[2],x);solve(li[3],x);

- Given the expression
,
- A)
- Plot the expression and in text state how many times the it crosses the x-axis.(Experiment with domain values until you find values that show the crossing points clearly.)
- B)
- Use the Maple
`solve`command to find the values of where it crosses the x-axis (also called the roots). - C)
- Use the Maple
`fsolve`command to find the roots. - D)
- State, in text, the value of the roots. Also, how are the results of
`solve`and`fsolve`different in this problem?

- Given the functions
and
- A)
- Plot the functions. Again experiment with domain values until the intersection points are clear. Then state in text how many intersection points you see.
- B)
- Using the
`solve`command find the intersection points.Label the values by giving the`solve`command a name. How many values does the`solve`command find? - C)
- Use the
`fsolve`command to find the rest of the answers. Label the values by giving each`fsolve`command a name. - D)
- Find all the values and state the intersection points in text.(When writing your text sentence use only two decimal places for the numbers. Round correctly!)

- Find the intersection point of the three planes , , and . First plot the planes over the domain and .

2013-09-11