Special Trigonometric  Limits

    This topic states the limits of the trigonometric functions and also two very useful limits involving sine and cosine. These special limits can either be proved with L'Hopitals rule or with the squeeze rule. Examples are given which illustrate there usefulness.

Proposition (Special Trigonometric Limits) The following trigonometric limits hold:

Example (Special Trigonometric Limits) Find the limit:

    Solution. We have
    


Example (Special Trigonometric Limits) Find the limit:

    Solution. We have

Example (Special Trigonometric Limits) Find the limit:

    Solution. We have

Example (Special Trigonometric Limits) Find the limit:

    Solution. We have







(using and since as we infer that so we continue)

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