149 Math Lab 1 - Exercises
Name: < your name goes here >
Section: < your section number goes here >
Exercises
Exercise 1: Solving a System of Equations
Given the system of equations:
y=2x+2
y = 2 x3 + 7 x2 - x - 2
Find the three solutions via the following four methods, and compare your results:
Graphically, by plotting the two expressions and estimating the points of intersection.
Through the use of the Solve command.
Through the use of the Reduce command.
Through the use of the NSolve command.
Useful commands for this exercise:
Plot[{function1name[variable],function2name[variable]},{variable,leftborder,righ
tborder},PlotRange->{lowborder,highborder}, PlotLabel->Title] plots two functions and
explicitly gives the range of coordinates over which to plot. It also allows you to specify a title.
Solve[{expression1==expression2,
expression3==expression4},{variable1,variable2}] solves symbolically for the situation where
expression1 is equal to expression2 and expression3 is equal to expression4.
Reduce[{expression1==expression2,
expression3==expression4},{variable1,variable2}] solves symbolically for the situation where
expression1 is equal to expression2 and expression3 is equal to expression4.
NSolve[{expression1==expression2,
expression3==expression4},{variable1,variable2}] numerically solves for the situation where
expression1 is equal to expression2 and expression3 is equal to expression4.
Exercise 2: Fun with Plots and Functions
Consider the function f(x) = 1 + x
1+4x .
Plot the graph of f and the the graph and the ability to zoom in to find the domain, range, and zeros of f.
Useful commands for this exercise:
2
Math 149 Lab 1 Exercises.nb
Plot[functionname[variable],{variable,leftborder,rightborder},PlotRange>{lowborder,highborder}, PlotLabel->Title] plots a function and explicitly gives the range of
coordinates over which to plot. It also allows you to specify a title.
Plot[{function1name[variable],function2name[variable],function3name[variable]},
{variable,leftborder,rightborder}, PlotStyle>{{Color1,Dotted1},{Color2,Dotted2},{Color3,Dotted3}}, PlotRange>{lowborder,highborder}, PlotLabel->Title,] plots three functions and explicitly gives the range of
coordinates over which to plot. It also specifies color and dotted information and includes a title.
Exercise 3: Polynomial roots
Find all real zeros of the polynomial q(x) = 19 5 x + 8 x3 + 3 x6 .
Useful commands for this exercise:
Plot[expression,{variable,leftborder,rightborder}] plots an expression in one variable over a
region.