Limit Laws
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Limit Laws
Objectives
- Recognize the basic limit laws. Use the limit laws to evaluate the limit of a function.
- Evaluate the limit of a function by factoring.
- Use the limit laws to evaluate the limit of a polynomial or rational function.
- Evaluate the limit of a function by factoring or by using conjugates.
- Evaluate the limit of a function by using the squeeze theorem.
In the image above, the Limit Laws below describe properties of limits which are used to evaluate limits of functions.
- Sum law for limits states that the limit of the sum of two functions equals the sum of the limits of two functions.
- Difference law for limits states that the limit of the difference of two functions equals the difference of the limits of two functions.
- Constant multiple law for limits states that the limit of a constant multiple of a function equals the product of the constant with the limit of the function.
- Product law for limits states that the limit of a product of functions equals the product of the limit of each function.
- Quotient law for limits states that the limit of a quotient of functions equals the quotient of the limit of each function.
- Power law for limits states that the limit of the nth power of a function equals the nth power of the limit of the function.
- Root law for limits states that the limit of the nth root of a function equals the nth root of the limit of the function.