Limits of trigonometric functions
         Evaluating trigonometric limits, examples
      Limits of functions based on the definition of the natural number e
         Evaluating limits of functions based on the definition of the natural number e
Evaluating trigonometric limits, examples
We use the fundamental limit and known trigonometric identities when solving trigonometric
limits.
Example:  Evaluate the limit  
Solution:  
Example:  Evaluate the limit  
Solution:   Since  cos (a + b) = cosa cosb - sina sinb   then   cos2a = cos2a - sin2a = 1 - 2sin2a
that is    
Example:  Evaluate the limit  
Solution:   We use the sum to product identity and the fundamental trigonometric limit, thus
Example:  Evaluate the limit  
Solution:   If we substitute  arcsin (x + 2) = t   then,
x + 2 = sin t  or  x = sin t - 2  so that,   t as x -2,  therefore
Evaluating limits of functions based on the definition of the natural number e
Use    to evaluate limits of the form
Example:  Evaluate the limit  
Solution:    
Example:  Evaluate the limit  
Solution:  
 
Calculus contents B
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