MATA32H3 Lecture Notes - Lecture 5: Logarithmic Differentiation, Marginal Revenue

• School: UTSC
• Department: Mathematics
• Course: MATA32H3
• Professor: Xiamei Jiang

Document Summary

Let p be the price per unit of a product and q be the quantity of units demanded. Let the demand function p = f(q) be differentiable. Example 5. 1: the demand function for a manufacturer"s products given by p = 300 q2, where p is the price per unit when q units are demanded. Find the point elasticity of demand when q = 5, 10, 15 separately. Example 5. 2: find y if y = xx. Example 5. 4: find y : y = (x2 4)5(3x + 5)4. Suppose that we wish to find the roots of f(x) = 0. We begin with choosing a value x0 as our initial guess and use the formula to obtain our second guess and repeat the procedure, which will result in x2, x3, and so on. The value of xn+1 is then given by for n = 0, 1, 2, . This produces a sequence of numbers x0, x1, x2, x3, .