This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Part I Math 165 Final Exam (II) Spring 2003 1. Given f ( x ) = x +1 x 1 x ≤ x 1 x +1 x > Which of the following statements are true? I f is discontinuous at x = 1 II f is discontinuous at x = 0 III f is discontinuous at x = 1 IV lim x → f ( x ) = 1 V lim x → 1 f ( x ) = 0 (a) only I, III, V (b) only I, II, III (c) only I, II, III, IV (d) only II, V (e) only IV, V (f) only V (g) none of the above 2. f ( x ) = √ x +1 1 x , find lim x → f ( x ) . 3. (a) Find the critical points of the function f ( x,y ) = x 3 + y 3 6 xy and classify each as a relative maximum, a relative minimum, or a saddle point. (b) repeat for f ( x,y ) = 4 x 3 12 y 2 + 24 xy + 10 4. A manufacturer can produce blank videotape cassettes at a cost of $2 apiece. The cassettes have been selling for $4 apiece, and at this price, consumers have been buying 4,000 cassettes a month. The manufacturer is planning to raise the price of the cassettes and estimates that for each $1 increase in the price, 400 fewer cassettes will be sold each month. At what price should the manufacturer sell the cassettes to maximize profit? 5. A manufacturer finds that in producing x units per day (for < x < 100 ), three different costs are involved: a fixed cost of $1,200 per day in wages, a production cost of $0.20 per day for each unit produced, and an ordering cost of 100 x 2 dollars per day. Determine the level of production that results in minimal total cost per day. 6. For some f ( x ) , f ( x ) = 3 x 2 2 x 3 . Find the relative extrema of f . 1 7. At a certain factory, the total cost of manufacturing q units during the daily production run is C ( q ) = 0 . 2 q 2 + q +900 dollars. From experience it has been determined that approximately q ( t ) = t 2 +100 t units are manufactured during the first t hours of a production run. Compute the rate at which the total manufacturing cost is changing with respect to time 1 hour after production commences.production commences....
View
Full
Document
This note was uploaded on 09/09/2010 for the course MATH 165 taught by Professor Staff during the Spring '08 term at Ill. Chicago.
 Spring '08
 STAFF
 Math, Calculus

Click to edit the document details