HW5: Prove that the interval U=(5,9) is an open set on the real line. Hint: You will need to choose an r_p small enough so that your ball stays under 9 and above 5. To do this you will taking a minimum of two different formulas. This is similar to the minimum used in the video proving intersections of open sets are open. Again you may have difficulty guessing a formula, so instead start writing the proof and figure it out from the bottom up: 1. Given any p in U we choose r_p=. 2. Given any x in B(p,r_p) we have x in (p-r_p, p+r_p) (2) B(p,R)=(p-R,p+R) 3. p-r_p0 and justify why this is greater than zero carefully. And then complete your proof downward. _>0 (1) explain why r_p>0 here
Quadratic Equation
When it comes to the concept of polynomial equations, quadratic equations can be said to be a special case. What does solving a quadratic equation mean? We will understand the quadratics and their types once we are familiar with the polynomial equations and their types.
Demand and Supply Function
The concept of demand and supply is important for various factors. One of them is studying and evaluating the condition of an economy within a given period of time. The analysis or evaluation of the demand side factors are important for the suppliers to understand the consumer behavior. The evaluation of supply side factors is important for the consumers in order to understand that what kind of combination of goods or what kind of goods and services he or she should consume in order to maximize his utility and minimize the cost. Therefore, in microeconomics both of these concepts are extremely important in order to have an idea that what exactly is going on in the economy.
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