Computing Limits

    In this topic we illustrate how to compute limits by working out several examples using factoring, trigonometry, and rationalization. We also work on limits of piecewise functions.

Example (Finding Limits Using Algebra) Compute the limit of at

    Solution. We have

Example (Finding Limits Using Algebra) Given and compute the limit at

    Solution. The graph of is



which inspires to try a factor of from obtaining and a graph of is


which also inspires to try to factor of from obtaining Therefore,

Example (Finding Limits Using Trigonometry) Compute the limit of at

    Solution. We have

Example (Finding Limits By Rationalizing) Compute:
    
    Solution. We have
    

Example (Finding Limits By Rationalizing) Compute the limit of at

    Solution. We have

Example (Finding Limits By Rationalizing) Compute   

    Solution. We have
    
    
    
    
    
    
    
    
    
    
    
    

Example (Finding Limits By Rationalizing) Compute the limit of at

    Solution. We have

Example (Finding Limits of Piecewise Functions) Find the limit,



    Solution. We have  
    

Example (Finding Limits of Piecewise Functions) At compute the limit of



    Solution. We have and Therefore, even though

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Cite this as:
Computing Limits
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/computing-limits.html