Difference between revisions of "009A Sample Final 1, Problem 1"

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!Final Answer:    
 
!Final Answer:    
 
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|'''(a)'''&thinsp; <math style="vertical-align: 0px">9</math>
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|&nbsp;&nbsp; '''(a)'''&thinsp; <math style="vertical-align: 0px">9</math>
 
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|'''(b)'''&thinsp; <math style="vertical-align: 0px">+\infty</math>
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|&nbsp;&nbsp; '''(b)'''&thinsp; <math style="vertical-align: 0px">+\infty</math>
 
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|'''(c)'''&thinsp; <math style="vertical-align: -15px">-\frac{3}{2}</math>
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|&nbsp;&nbsp; '''(c)'''&thinsp; <math style="vertical-align: -15px">-\frac{3}{2}</math>
 
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[[009A_Sample_Final_1|'''<u>Return to Sample Exam</u>''']]
 
[[009A_Sample_Final_1|'''<u>Return to Sample Exam</u>''']]

Revision as of 15:12, 18 April 2016

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