Lab 1: Last partRecall that we have had two previous assignments to do for the first lab. The first wasa list of LATEXcommands to look up, a short paper about arc length with some specificLATEXthings to include, and today we will be solving some short problems using Maple.Lab 1 is all three parts- Our previous two assignments, together with today’s introductionto Maple questions. Here is what to turn in (BEFORE our next lab meeting):For your group, one person will email me the following (email address: [email protected],subject line: Math 235X (or Math 235Y), Lab 1):• The latex file answering the questions for our first assignment (the .tex file ONLY).• The latex file for the Arc Length question.• The Maple file that answers the questions on the next page (not the introduction).Remove all the Maple output before mailing the worksheet file:Edit⇒ Remove Output⇒ From WorksheetGrading criteria: 5 pts per item below• Lab 1a: Look things up in the LaTeX manual. I will be looking at your tex file to besure the commands are correct.• Lab 1b: The article we started last time (see that lab for grading criteria). Here,I am looking to see if the mathematics is correct, well typeset, and that the LaTeXspecifications are included and correct.• Maple Worksheet: Be sure that your Maple commands will work from scratch, andthat they answer the four questions attached.Today’s Maple Lab (Lab 1, Part cWork through the Introduction to Maple before answering the following questions. Tryusing Maple’s help features before asking your instructor for assistance.On a new Maple worksheet (different than the one used for the Introduction), answer thefollowing “typical” Calculus questions:1. Use the Maple help system to find out how to enter a vector and compute the followingcross product:h1, 1, 1i × h1, 2, 3iHint: Try looking under Tools -> Tasks -> Browse... Then see if you can find thecross product. The cross product is “vector algebra”, done in “vector calculus”.2. Let f(x) = e−(x−3)2/6. Get a numerical approximation to the integral:Z10−10f(x) dxHints:• What is the difference between int and Int?• The exponential function is exp(x), not e^x3. Look up how to compute the Taylor approximation (include terms to t6) then do itfor:f(t) =Zt1cos(u)uduat t = 1. Plot the Taylor approximation (up to t6term) for 1/2 ≤ t ≤ 3/2, then plotthe error on the same interval.4. Look up, then find the derivative of f(x) =1xby using Maple to step through thedefinition of the derivative, that is,f0(x) = limh→0f(x + h) − f(x)hOnce you have an answer for that function, copy and paste to do the same thing forg(x)