Introduction to Maple: Part IMaple is a comprehensive computer algebra system (CAS). A CAS has the capability of performing complex symbolic manipulations and producing high quality mathematical graphics and animations. In this project you will be introduced to the basics of Maple input and Maple syntax.Note that in all projects the executable Maple commands will be displayed in red and will be proceeded by the > symbol, Maple output will be displayed in blue, and directions and comments will be displayed in black or green. Green will be reserved for important notes and warnings such as the following. You may simply press enter at any point on a line containing a Maple command to execute that command. The cursor will automatically jump to the next Maple command line. You may also click on a command line to position the cursor there.Click on the gray box containing the + symbol beside the section entitled Maple Input below to begin. This will reveal the relevant material on this topic. You can click the gray box a second time to hide this material.

Every Maple command must be terminated with a semicolon (;). Press enter on the commands that follow to see how each affects the Maple output.5+10;5+10Note that when the second command was executed, Maple provided an error statement indicating that the command was incorrectly entered. Click on the command line above, insert the semicolon, and execute the command again.

As suggested by the example above, the standard arithmetic operations may be performed using the standard mathematical symbols: addition +subtraction -multiplication *division /exponentiation ^ or **Execute the commands that follow.2^20;2/3+1/4;Use Maple to compute NiMsKCIiIyIiIi0iIiU2I0YkRiUqJkYnRiUqJEYkRiQhIiJGKw== on the command line that followsMaple does not allow for "implied" multiplication; every multiplicative operation must be explicitly denoted using the * symbol. Press enter on the command that follows and correct the command as the Maple output suggests.3x;Maple will perform operations using the standard order of operations: parentheses, exponents, multiplication & division, addition & subtraction. Use an abundance of parentheses to ensure that Maple is outputting the desired result. Press enter on the following commands and attempt to determine which correctly 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25(2^6*0.5);25*2^(6*0.5);25*2^6*0.5;

The first command is missing the explicit multiplication symbol *. The second command is the proper syntax for this computation. The third command is the syntax for computing NiMqJi0iI0Q2IyokIiIjIiInIiIiLUkmRmxvYXRHSSpwcm90ZWN0ZWRHRi02JCIiJiEiIkYq.

Use Maple to compute NiMqJiwmKiQiIiMiIiciIiIiIikhIiJGKCwmIiIlRihGJkYoRio= on the command line that follows (the correct answer is 4). Do not simplify by hand first.

Many standard mathematical constants and functions are preprogrammed in Maple. The following list contains those that should be familiar from your Precalculus courses.Mathematical Expression Maple Input NiNJI1BpR0kqcHJvdGVjdGVkR0Yk Pi; NiNJKWluZmluaXR5R0kqcHJvdGVjdGVkR0Yk infinity; NiMtSSVzcXJ0RzYiNiMsJCIiIiEiIg== or i I; NiMpSSJlRzYiSSJ4R0Yl exp(x); NiMtSSNsbkc2IjYjSSJ4R0Yl ln(x); NiMtSSRhYnNHSSpwcm90ZWN0ZWRHRiU2I0kieEc2Ig== abs(x); NiMtSSVzcXJ0RzYiNiNJInhHRiU= sqrt(x); NiMtSSRzaW5HNiI2I0kieEdGJQ==, NiMtSSRjb3NHNiI2I0kieEdGJQ==, etc. sin(x); cos(x); etc. NiMtSSdhcmNzaW5HNiI2I0kieEdGJQ==, NiMtSSdhcmNjb3NHNiI2I0kieEdGJQ==, etc. arcsin(x); arccos(x); etc.Use Maple to compute NiMtSSVzcXJ0RzYiNiMsJCIjRCEiIg==, NiMtSSRzaW5HNiI2IyooIiM2IiIiSSNQaUdJKnByb3RlY3RlZEdGK0YpIiIjISIi, and NiMtSSRleHBHNiI2Iy1JI2xuR0YlNiMiIig= on the command lines that follow.As stated in the list above, the value NiNJI1BpR0kqcHJvdGVjdGVkR0Yk is defined by Pi in Maple. Press enter on the command line that follows.pi;Though Maple outputs NiNJI1BpR0kqcHJvdGVjdGVkR0Yk , this is the Greek letter NiNJI1BpR0kqcHJvdGVjdGVkR0Yk and not the number NiNJI1BpR0kqcHJvdGVjdGVkR0Yk = 3.14159.... This example shows that Maple is case-sensitive: Pi is not the same as pi. Other instances where important differences in commands depend on case will be denoted in future projects. Note that sin(x) is not the same as sin*(x) although the Maple output from the next two lines might seem to suggest otherwise. The first command line is the correct input as shown in the list provided above.sin(x);sin*(x);Now consider inputing the square of a trigonometric function such 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This has to be entered as shown on the first command line that follows not in the form that it is written on the second command line that follows.(sin(3*Pi/2))^2;sin^2(3*Pi/2);

You can often use the percent symbol (%) as a shortcut when entering input. Maple interprets the percent symbol to represent the output from the most recently executed command.1/2+3/4;%*4;Maple will recall the most recently executed command when % is used, which will not necessarily be the output from the previous line if the commands were not executed in order. For example, execute the first command that follows, then the third command that follows, and finally the second command that follows and note the output.sqrt(4);%/2;abs(-10);

Maple will give exact output unless decimal values are input. Note the difference in the output from Maple on the following two lines. 1305/722;1305/722.0;We can also obtain approximate decimal values from exact values by using the evalf command as demonstrated below.sqrt(2);evalf(%);As you can see in the above output, Maple uses a default of 10 digits in its output of numerical values. We can control the number of digits in the output using the commands displayed below.evalf(1305/722,4); evalf(1305/722,50); Use Maple to approximate NiMtSSR0YW5HNiI2IyooIiIkIiIiSSNQaUdJKnByb3RlY3RlZEdGK0YpIiIoISIi to 7 decimal places on the command line that follows (you will need a total of 8 digits).

Open and complete the Introduction: Part I worksheet (Microsoft Word document) found in the same folder from where you downloaded this file. You may use Maple to help you complete the assignment.