Download Justify - Calculus - Exam and more Exams Calculus in PDF only on Docsity!
Simon Fraser University Math 151-3, Spring 2004 Test 2 (Grey version)
Time: 50 minutes 10 March 2004
Last Name Given Names
Student Number
Instructions
- Do not open this test booklet until instructed to do so.
- Print your name and write your student number above.
- The possession of any calculators in this test is considered as academic dishonesty.
- Full marks will be awarded for correct, complete and well-organized solutions.
- You may use the back of any page for rough work.
- There are 6 pages in this test booklet.
Question Marks
Total /
- Find the following limits if they exist. Show and justify your work.
(a) [4 marks] lim x→ 4 +
x − 4 √ x − 2
(b) [4 marks] lim x→∞
ln (5 + x) x + ln x
- (a) [4 marks] Let f (x) = 2x^3 + 5x^2 − 12 x − 11. The equation
f (x) = 0
has a solution near x 1 = 2. Use Newton’s Method to find a better approximation x 2 of the solution to this equation. Express your answer as a fraction.
(b) [4 marks] Find
dy dx
if x^3 = 5x^2 y + 2y^3.
- Let P be a point on the curve of the function y =
5 x, and let s be the distance between P and the origin (0, 0).
(a) [2 marks] Express s as a function of the x-coordinate x of P.
(b) [4 marks] Suppose the x-coordinate of P increases at a constant rate of
14 units per second. How fast is s changing when the x-coordinate of P is 2 units?
