Lab 1 - Monday January 24: Learning to use MapleThe following example illustrates the commands that you will need for the two exercises at the end of this lab session. This lab is intended to give you an introduction to MAPLE and you need to turn in a hard (paper) copy of your lab. If two of you work together, you must turn in ONLY ONE COPY WITH BOTH OF YOUR NAMES ON IT. This lab is due in your recitation section on Thursday 1/27.Examples1. The first thing you should learn to do is to insert text into your MAPLE session. This is easy. Just click on the [> button and then click on the T button on the toolbar. Try this out now and include the following information as text at the top of your Maple lab: Name(s), Lab 1, Date, Section #.If you want to delete a region defined by the various sized [ , just put your cursor in that region and hit Cntrl, Delete.2. You also need to know how to enter a function into Maple. Let's enter the function NiMvLSUiZkc2IyUieEcsKiokRiciIiUiIiIqJiIiI0YrKiRGJ0YtRishIiIqJkYqRitGJ0YrRisiIiZGKw== into Maple. To do this we need a Maple input line that starts with > . To get such a line, hit the [> button, issue the command below and hit Enter.f:=x^4-2*x^2+4*x+5;We can ask Maple for particular values of the function using the subs command. I would like to calculate f(3/2). NOTE that I am going to give the result the name a.a:=subs(x=3/2,f);evalf(a);The evalf command will turn a non-decimal value into a decimal value.3. To plot f(x) over the interval [-2,2] we use the plot command.plot(f,x=-2..2);It is a good idea to shrink the picture of the plot before printing you session (please shrink your plots to conserve paper - yes, I am a tree hugger). Do this by left-clicking on the graph to get a box with little black squares on the corners (i.e. frame the graph). Then grab a corner of the plot (left-click hold) and shrink it down by dragging.If you want to restrict the y-axis in the plot to a certain interval, say y = 5 to y = -2, just use the commandplot(f,x=-2..2,y=-2..5);You are expected to try various x and y ranges before deciding on the one that best frames the picture. To do this, go back to the SAME plot statement and vary the x and y values and hit enter again. This will make Maple replot the graph with those domain and range values. Usually there is no reason for you to retype a new plot line and create a new graph, rather just update and hit enter on the ONE graph.4. Let's find all points where f(x)=0 by using the fsolve command. These are the points where the graph intersects the x axis (also known as the x-intercepts). These points have a y value of zero.fsolve(f=0,x);For polynomial equations, Maple usually returns all the roots. In this case there are two roots and they are given in a "list". To use these values in other equations, we need to name them. The easiest way to do this is to limit the domain over which the fsolve command searches for the value. By looking at the graph we can see the values or by looking at the fsolve solution above. Please be warned that Maple will not allways find more than one root using the fsolve command as I did above even if more than one answer exists. Thus, you should look at the graph and do a limited domain to find all the roots as I do below.x1:=fsolve(f=0,x=-2..-1.5);x2:=fsolve(f=0,x=-1.5..0);5. Maple is great for doing trig! You enter trig functions just as you would expect. But please be warned that Maple expects the argument of a trig function to be given in RADIANS. To enter a radian value with pi in it, you enter "Pi" exactly like that....Capital P and lower case i.g:=tan(x);To evaluate tangent at 180 degrees.....b:=subs(x=Pi,g);evalf(b);You can enter any sort of trig function with any of the following (sin(x), cos(x), tan(x), cot(x), sec(x), csc(x)) and have Maple convert it to an expression with only sines and cosines. The command to do this is convert. The first argument in the convert command is the name of the function that you would like to convert to having only sines and cosines and the second argument is always "sincos".h:=(csc(x))^2-2*sin(x)*tan(x);hnew:=convert(h,sincos);Now work the exercises. Be sure to save your session frequently so that if your system crashes, you have most of your work saved. Use the Save As option under the File button to name and save a file.Exercise 1.Let NiMvLSUiZkc2IyUieEcsLCIjPSIiIiomIiM3RipGJ0YqISIiKiYiIilGKiokKUYnIiIjRipGKkYtKiYiIiRGKiokKUYnRjRGKkYqRioqJClGJyIiJUYqRio= .(a) Enter f(x) into Maple.(b) Construct a plot of f(x) over [-5,5].(c) Construct a plot of f(x) over [-5,5] with the y-axis restricted to y = -25 to y = 25.(d) Find all solutions to f(x)=0.Exercise 2. Consider the function NiMvLSUiZ0c2IyUieEcqJiIiIyIiIi0lJHNpbkc2IyomRilGKkYnRipGKg==(a) Enter g(x) into Maple. Since you entered f(x) in the previous exercise with the name f, Maple will remember that function as f so we give a new name to this function, say g.(b) Construct a plot of g(x) and f(x) on the same axis using the command plot({f,g},x=-5..5);(c) Find all the points where f(x)=g(x) using the fsolve command. Be sure to give the x and y coordinates of ALL the points where f(x)=g(x). Remember, if you name x1 as the x-coordinate then you can find the y-coordinate using the subs command.(d) Evaluate the function g(x) at the following values using the Maple subs command, and possibly the evalf command: 30 degrees, 45 degrees, 60 degrees, 90 degrees, 120 degrees, 330 degrees.