WARNING: THIS IS NOT THE ACTUAL MIDTERM IT IS JUST TO MAKE YOU FAMILIAR WITH THE FORMAT Sample Exam for Multivariable Calculus but with material from Calc1 and Calc2 NAME: RUID: EMAIL: BELOW WRITE THE LIST OF THE ANSWERS Answer[ 1 ]= Answer[ 2 ]= Answer[ 3 ]= Answer[ 4 ]= Answer[ 5 ]= Answer[ 6 ]= Answer[ 7 ]= Answer[ 8 ]= Answer[ 9 ]= Answer[ 10 ]= ----------------------------------------------------------------- Instructions: Download this file with its original name, mt1.txt, then rename it, in your computer mt1FirstLast.txt Edit it with your answers and solutions and Email DrZcalc3@gmail.com, 80 minutes (or sooner) after starting (for most people 10:00am, Oct. 15) Subject: mt1 with an attachment. YOU MUST NAME IT EXACTLY mt1FirstLast.txt --------------------------------------------------------------------------- For each of the questions you MUST first figure, YOUR version, with the following convention For i=1,2,3,4,5,6,7,8,9 , a[i]:= The i-th digit of your RUID, BUT of it is zero make it 1 Example: RUID=413200125; a[1] = 4, a[2] = 1, a[3] = 3, a[4] = 2, a[5] = 1, a[6] = 1, a[7] = 1, a[8] = 2, a[9] = 5 HERE WRITE THE ACTUAL a[i] a[1] = , a[2] = , a[3] = , a[4] = , a[5] = , a[6] = , a[7] = , a[8] = , a[9] = -------------------------------------------- --------------------------------------------- Problem 1: Let P1=(a[1],a[3]), P2=(a[5],a[7]), P3=(a[9],a[1]), P4=(a[4],a[3]) Find the x-coordinate of the point of intersection of the line joining P1 and P2 and the line joining P3 and P4 With my RUID data the question is Here is how I do it (Explain everything) Ans.: --------------------------------------------- Problem 2: Find the y-coordinate of the inflection point of the function f(x):= 3 2 x a[4] - x a[1] + x a[2] - a[9] With my RUID data the question is Here is how I do it (Explain everything) Ans.: --------------------------------------------- Problem 3: Find the absolute maximum value of f(x):= 2 x a[7] + x a[5] - a[4] In the closed interval 0<=x<=4 With my RUID data the question is Here is how I do it (Explain everything) Ans.: --------------------------------------------- Problem 4: Find f''(a[3]) if f(x)= exp(exp(x)) With my RUID data the question is Here is how I do it (Explain everything) Ans.: --------------------------------------------- Problem 5: Use Newton's rule to approximate (a[3]^(a[4]+1)-1)^(1/(a[4]+1)) With my RUID data the question is Here is how I do it (Explain everything) Ans.: --------------------------------------------- Problem 6: Find the area under the curve y = a[1]*x^3 + a[5]*x^2+ a[2]*x+a[9] between the vertical lines x=0 and x=1 With my RUID data the question is Here is how I do it (Explain everything) Ans.: --------------------------------------------- Problem 7: Find the area under the curve y = ( (a[1]+a[2])*x - (2*a[1]+a[2]))/(x^2-3*x+2) between the vertical lines x=3 and x=4 Leave your answer in terms of log (or ln), i.e. do not convert if to decimals With my RUID data the question is Here is how I do it (Explain everything) Ans.: --------------------------------------------- Problem 8: Find the slope of the tangent line to the curve a[1]*x^2+ a[7]*x*y+ a[8]*y^2= a[1]+a[7]+a[8] at the point (1,1) With my RUID data the question is Here is how I do it (Explain everything) Ans.: --------------------------------------------- Problem 9 Find the coefficient of x^2 in the Taylor series around x=0 or the function f(x)= (1+x)^a[9] With my RUID data the question is Here is how I do it (Explain everything) Ans.: --------------------------------------------- Problem 10 Find the coefficient of x in the Taylor series around x=0 or the function f(x)= (1+x)^(1/(a[9]+1) ) With my RUID data the question is Here is how I do it (Explain everything) Ans.: