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Unformatted text preview: 1. Domain and range of a function Example : find the domain and the range of the functions 2 2 1 4 7; 1 x x- +- . 2. Equations - Simultaneous equations Example : find the solutions of equations or simultaneous equations 3. Demand and supply model - Keep in mind that quantities and prices are always nonnegative numbers.- Equilibrium point: the intersection point of demand and supply curves Example : Find the equilibrium price and equilibrium quantity of a demand and supply model. 4. Sequences, Series and Limits- Sandwich theorem- Basic property: If the series n x is convergent we must have lim n n x = . Example : Consider the convergence of the following series 2 2 3 1 1 n n n n =- +- , we find that 2 2 2 2 1 1 3 3 1 3 1 1 1 n n n n n n x n n - +- + = = -- . Hence, we conclude that the series is divergent. Remember that if lim n n x = , we can't conclude immediately that the series n x is convergent. However, if the series n x is convergent we must have...
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- Spring '12