MATH 2825
NAME:
Mathematica Lab #4
Due Monday December 5th 2022 by 11:30 A.M.
All work is to be done in a programming notebook either Mathematica and Jupyter (python3).
Please refer to the blackboard site for commands and examples.
Submissions must be made electronically on blackboard, consider using a GitHub repository to store your code.
You will be graded on the output that I am able to generate from your commands.
1. Let a be the digit corresponding to the last digit of your student id number, if it is 0 use 10. Consider the function
f (x) = x6 ? x5 ? ax4 ? x2 + x ? 1
(a) Graph the function on an interval so that you can approximate the roots of the function. State your
approximations clearly.
(b) Use a built-in command to find all roots. These built-in command may use Newtonàmethod to solve for
roots.
2. Consider the curve y = xa , where a is defined as above except if 1 use 11.
(a) Graph the equation from 0 to 2.
(b) Express the area under the curve as a limit and compute this limit.
(c) Check your answer by using a definite integral. Explain in words why these must be the same.
3. Consider the function,
Z x
Si(x) =
0
sin t
dt
t
(a) Plot Si(x) for 0 ? x ? 20.
(b) Find the values for x where there are local extrema, explain in words where all values would be.
(c) Solve Si(x) = 1.

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