Ch 1. Limits Multimedia Engineering Math Limit of aSequence Limit of aFunction LimitLaws Continuity RateChange
 Chapter 1. Limits 2. Derivatives I 3. Derivatives II 4. Mean Value 5. Curve Sketching 6. Integrals 7. Inverse Functions 8. Integration Tech. 9. Integrate App. 10. Parametric Eqs. 11. Polar Coord. 12. Series Appendix Basic Math Units Search eBooks Dynamics Fluids Math Mechanics Statics Thermodynamics Author(s): Hengzhong Wen Chean Chin Ngo Meirong Huang Kurt Gramoll ©Kurt Gramoll

 MATHEMATICS - THEORY Limit Laws Limit Laws are the properties of limit. They are used to calculate the limit of a function. Constant Law The limit of a constant is the constant itself.       Sum law (Law of addition ) The limit of a sum is the sum of the limits.       Difference Law (Law of subtraction) The limit of a difference is the difference of the limits.       Constant Multiple Law The limit of a constant times a function is the constant times the limit of the function.       Product Law (Law of multiplication) The limit of a product is the product of the limits.       Quotient Law (Law of division) The limit of a quotient is the quotient of the limits (provided that the limit of the denominator is not 0).       if       Special limit The limit of x is a when x approaches a.       Power law The limit of the power of a function is the power of the limit of the function.       if n is a positive integer. Power special limit The limit of x power is a power when x approaches a.       if n is positive. Root special limit       where n is a positive integer. If n is positive, then it is assumed that a > 0. Root law       where n is positive integer. It is assumed that       if n is even. Left and Right Hand Limit Left hand limit example Left hand limit: If f(x) is defined in an interval (a, b), and f(x) approaches A as x approaches b from the left side b, then Right hand limit example Right hand limit: If f(x) is defined in an interval (a, b), and f(x) approaches A as x approaches a from the right side a, then