Texas A&M University



plete Lab 9 in Python using the following hintsThis lab is the LAST LAB. No individual work will be accepted. Math 151 TAs (via Bcc):Teams will work together on the posted problems. Details on how to work on the problems and what to submit are explained in the "Overview" of the Lab Schedule ().?This lab focuses on L'Hospital's Rule, Applied Max/Min, and Antiderivatives (the last two being the focus of the overview posted at?).? Also, since the following week is Exam III and the week after that is split over the last 2 calendar weeks due to Thanksgiving, this is the FINAL lab assignment!?There are NO new commands in the assignment this week.? Here are the key Python commands used, along with links to the online help pagessymbols:?(Used to create symbolic variables.? NOTE: restrict the variables in #2 to be positive because of all the square roots involved.)limit:?(Used to find the limits in #1)print:?(All answers and explanations should be given using print commands.)diff:?(Needed for #1c and #2)simplify:?(Used to print the?simplified?f'/g' in #1c)Rational:?? (Reminder that when working with fractions in sympy, the Rational command is best so Python does not divide and create floating point values.? Used with the "8 1/2" dimension of the paper in #2)solve:?(Needed to set up and find the critical values in #2 and determine when the canister hits the ground-and the required v0-in #3)subs:?(Needed to set up and determine the y-value for the absolute extremum in #2)evalf:?(Used to find the floating point value of the answer in #2)integrate:?(Needed to find the antiderivatives in #3 as explained in the Overview)Other comments on individual problems:#1 Don’t forget that f '(x)/g'(x) limit is the limit of ln(y)-which is also a common mistake when doing these problems by hand!#2 You have the option of TRYING to set up the problem by hand (I don't recommend it) OR in Python.? If you get stuck on setting it up, the key is to define the horizontal fold as z, then recognize two things:?? a) The corresponding length z at the bottom is divided into two lengths which are sides of right triangles?? b) You can tell the other sides of those triangles since the given right triangle is congruent to the "folded out" triangle.So the maximum goal is from the Pythagoras Theorem, and the restriction is that z = the sums of the two legs.? Then solve the restriction for one variable and substitute into the goal.? Again, I did these things in Python because the algebra by hand is nasty.? IF you choose to go that route, you need to attach your work.? Once you have the area in terms of one variable, though, all remaining work should be done in Python.? Remember to print the results of the?solve?command before proceeding each time so that you know which element in the list of solutions is the correct one to use (which you should be able to tell by looking).#3 Introduces antiderivatives, or the?integrate?command.? While the actual integration is simple enough to do by hand, the algebra is not!? Also a good problem to get you ready Physics class next semester!?Let me know if you have any questions or comments about next week's lab which is the LAST LAB!? ................
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