17AMI.F09

# 17AMI.F09 - lim a n n" Justify your answer 6 Use log...

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

17A Midterm I (Benham) Fall 2009 1. a) Find the domain and range of f ( x ) = 4 x 2 ! x ( ) x + 3 ( ) b) Solve 3 x ! 5 " 4 2. A population triples every time step. a) Find its exponential model, given that the initial population is n 0 = 4 b) Find the recursion relation describing this model. 3. Determine the first four terms of the sequence defined by a n = n ! 1 ( ) n + 1 ( ) n 2 + 2 b) Find lim n !" a n : Justify your answer. 4. Use the Intermediate Value Theorem to determine whether the equation e ! x = x has a solution on the interval (0, 1). 5. The recursion relation a n + 1 = 3 a n 1 ! a n ( ) with a 0 = 1/ 3 defines a unique sequence. a) Find all fixed points for this recursion. b) Find
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: lim a n : n !" Justify your answer. 6. Use log transforms to change each of the following functions to a linear relationship. in each case determine whether a og – log or a log – linear plot should be used to graph that linear relationship. a) y = 3 e ! 2 t b) z = 2 x 3.5 7. Find the following limits. In each case, justify your answer. a) lim x !" 2 1 5 x 2 " 4 b) lim x ! sin 2 x x c) lim x ! 3 + x " 1 x 2 " 9 8. For each of the following functions, determine all values of f(x) where f(x) is continuous. a) f(x) == tanx b) f(x) = x 2 + x ! 6 x ! 2 c) f x ( ) = ln x ( ) x 2 + 1...
View Full Document

## This note was uploaded on 05/31/2011 for the course MATH 17A taught by Professor Lyles during the Spring '08 term at UC Davis.

Ask a homework question - tutors are online