Math 53 - Fall 2000 - Wagoner - Midterm 1

# Math 53 - Fall 2000 - Wagoner - Midterm 1 - Mathematics 53...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Mathematics 53 Midterm #1 , 27 Sept 2000 J .Wagoner Introduction Write your name, GSI’s name (5 points), and section number (5 points) on your Blue Book (5 points) right now. Partial credit may be given if your work justiﬁes it. Best wishes on the exam. Problem #1 From the diagrams below select the picture which best represents each of the following parametrized curves (A) a(t)=(cos(t)—1,sin(t)—t) (B) b(t)=(3¢os(t)+1,sin(t)—2) (C) c(t)=(t(t-1),t(t—l)(t-—2)) (D): d(t)=(cos(3t),sin(2t)) (E) c(t) = (e‘cos(t),e‘sin(t)) (F) f(t) = (t,t2 + sin(t)) 2 Problem #2 Consider the curve C deﬁned by r(t) = (cos3(t), sin3(t)) for 0 S t S 21r. (A) Which of the following two pictures best represents the part of the curve - for 0 _<_ t S 1r/2. Give a reason for your answer. Hint: Consider t = 1r/4. \I l l Y (z) (1) l ‘ ‘ x (B) Write down the formula for the length L of the curve C and use it to compute L. Problem #3 (A) Sketch the graph of r = 33in(29) where 0 S 0 5 271'. (B) Use small x’s to mark the portion of the curve corresponding to 61r/4 S 0 5 71r/4. Problem #4 (A) Sketch the graph of r = f (0) = 2/ sin(6) where 1r/4 _<_ 6 g 7r/2. (B) Sketch the region R consisting of those points (139) where 0 S r 5 f (0). (C) Compute the area of R. Problem #5 Consider the parametrized curve r(t) :2 (t + cos(t), 2t + sin(t)) where ~00 < t < 00. (A) For which values of it does the curve have a horizontal tangent? Explain. (B) For which values of t does the curve have a vertical tangent? Explain. Problem #6 Let P be the plane containing the three points A = (7, —3, —1), B = (1,0. 2), and C = (—1,—2,6). (A) Find a vector normal to the plane P and having length equal to 1. (B) Find the linear equation of the plane P. Problem #7 In R2 ﬁnd the orthogonal projection of v = (3,4) onto the line L which is perpendicular to 22: - y -— 1 = 0 and which passes through the origin 0 = (0,0). Problem #8 Compute the area A of the parallelogram determined by the vectors A = (3,2) and B = (2,1). ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern