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Math 251 Written Homework 2 - Fall 2017 Due Week 2 Page 1 of 1

Name:

Instructions: Put your solutions on a separate piece(s) of paper (8.5x11 or A4). Use this page as a cover sheet. Staple all of the pages together. Late homework is not accepted.

(1) Evaluate the following limit.

lim t→3

[( 4t−

2

t− 3

) ( 6 + t− t2

)]

(2) Give a formula for a function f that satisfies the following conditions. (The work you can show for this problem is: Show that your function satisfies all of the conditions.)

• lim x→4+

f(x) = −∞

• lim x→4−

f(x) = ∞

• f(0) = 0

(3) Determine the end behavior of the following function.

f(x) = ex + e2x

e2x + e3x

Hint 1: For the end behavior as x →∞ try dividing the numerator and denominator by e3x. Hint 2: For the end behavior as x → −∞ try dividing the numerator and denomi- nator by e2x.