009A Sample Midterm 3, Problem 1

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Find the following limits:

(a) If find

(b) Find

(c) Evaluate


Foundations:  
1. If , we have
       
2.


Solution:

(a)

Step 1:  
First, we have
       
Therefore,
       
Step 2:  
Since we have

       

Multiplying both sides by we get
       

(b)

Step 1:  
First, we write
       
Step 2:  
Now, we have

       

(c)

Step 1:  
First, we have
       
Step 2:  
Now, we use the properties of limits to get

       


Final Answer:  
    (a)    
    (b)    
    (c)    

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