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