limit examples
Example 1. Determine the limit . — Using the definition of and the limit rule of product (http://planetmath.org/LimitRulesOfFunctions) we can write
The limit in the former factor (http://planetmath.org/Product) is 1 by the parent entry (http://planetmath.org/LimitOfDisplaystyleFracsinXxAsXApproaches0). Also the latter limit is 1, since and thus the quotient is continuous in the point (see continuity of sine and cosine). Accordingly the desired limit is .
Example 2. Determine the limit . — As above, we can write
Example 3. The perimeter of a regular -gon, circumscribed to a circle with radius 1, is . Determine the limit of this perimeter as tends to infinity. — Utilising the example 1 we can calculate
which is the circumference of the circle.
Example 4. Determine the limit . — If we denote
the monotonicity of the arcus sine (http://planetmath.org/CyclometricFunctions) function on implies that “” is equivalent (http://planetmath.org/Equivalent3) to “”. Then we can calculate:
Example 5. One may use the definition of derivative in
Title | limit examples |
---|---|
Canonical name | LimitExamples |
Date of creation | 2013-03-22 17:40:16 |
Last modified on | 2013-03-22 17:40:16 |
Owner | pahio (2872) |
Last modified by | pahio (2872) |
Numerical id | 8 |
Author | pahio (2872) |
Entry type | Example |
Classification | msc 26A06 |
Classification | msc 26A03 |
Synonym | utilizing limit of in 0 |
Related topic | LimitRulesOfFunctions |
Related topic | DerivativeOfInverseFunction |
Related topic | ListOfCommonLimits |