Calculus 1 - Assignment 1

Calculus 1 - Assignment 1 - x ) . Problem 4: [4 points] Use...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Pawel Lorek, University of Ottawa, MAT 1330, Winter 2009 Assignment 1, due FEB 4, 17:30 in class Student Name Student Number Problem 1: [5 points] Suppose that at time t the population size of some individual is x t . Then, at time t + 1 each individual will produce 2 (1+0 . 01 · x t ) new ones (this quantity is called per capita production ). (a) Write the linear DTDS for the population size, x t +1 = f ( x t ) and ±nd x 2 when x 0 = 2. (b) Draw the updating function and start the cobwebbing process at 50 . (c) Find the equlibria explicitly. Problem 2: [4 points] Calculate the following limits (if left-side and right-side are di²erent, calculate both of them): (a) lim x →− 3 2 x + 5 ( x + 3) 3 , (b) lim x →∞ 2 x 4 - 6 x - 1 3 x 4 - 2 . Problem 3: [4 points] Use a calculator to guess the limits: (a) lim x 0 e 4 x - 1 2 x , (b) lim x 0 x sin(2
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: x ) . Problem 4: [4 points] Use the defnition oF the derivative to nd f ( t ), where f ( t ) =-2 t 2-4 t + 2. Calculate f (3). Problem 5: [4 points] The elevation of Ottawa River measured on JAN 20, 2009 was: the highest at 7:30 112.30 meters and the lowest at 13:30 - 111.70 meters. Assume that elevation has period 12h. Find the parameters in the standard cosine description of these tides, i.e., f ( t ) = A + B cos(2 ( t-) /T ) , where time t is measured in hours and t = 0 indicates midnight. Problem 6: [4 points] Explain why the following function is continuous. f ( x ) = e sin(2 x ) + 4 x 3 + 7 . Evaluate the limit lim x f ( x ) . 1...
View Full Document

Ask a homework question - tutors are online