{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Calculus 1 - Assignment 1

# Calculus 1 - Assignment 1 - x Problem 4[4 points Use the...

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

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 find 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 different, 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
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 π ( t-Φ) /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

{[ snackBarMessage ]}