009A Sample Final 1, Problem 1

From Math Wiki
Revision as of 11:57, 18 April 2016 by MathAdmin (talk | contribs)
Jump to navigation Jump to search

In each part, compute the limit. If the limit is infinite, be sure to specify positive or negative infinity.

a)
b)
c)
Foundations:  
Recall:
L'Hôpital's Rule
Suppose that   and   are both zero or both
If   is finite or 
then

Solution:

(a)

Step 1:  
We begin by factoring the numerator. We have
So, we can cancel   in the numerator and denominator. Thus, we have
Step 2:  
Now, we can just plug in   to get

(b)

Step 1:  
We proceed using L'Hôpital's Rule. So, we have
Step 2:  
This limit is 

(c)

Step 1:  
We have
Since we are looking at the limit as goes to negative infinity, we have
So, we have
Step 2:  
We simplify to get
So, we have
Final Answer:  
(a)
(b)
(c)

Return to Sample Exam