11Arev6 - ucsc econ/ams 11b Review Questions 6 fall 2008...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ucsc econ/ams 11b Review Questions 6 fall 2008 Implicit differentiation and Taylor polynomials 1. Use implicit differentiation to find the indicated derivative at the given point. dy at the point (1, 2) on the graph of the equation x3 y +2xy 3 − 4x2 y 2 = 2. dx du at the point (2, e) on the graph of the equation u2 ln v + v 2 e−u = 5. b. Find dv a. Find 2. Find the equation of the tangent line to the graph of the equation x3 y + 2xy 3 − 4x2 y 2 = 4 at the point (2, 1) on the graph. Note: You can use most of your work from problem 1a. here, but not all of it. 3. The demand equation for a firm’s product is given by p2 q + 2pq 3/2 + 3q 2 = 42500, where p is the price per unit for the firm’s product and q is the quantity demanded of the firm’s product. a. Find the price elasticity of demand for the firm’s product when p = 5 and q = 100. b. Estimate the percentage change in demand for the firm’s product, if they raise the price from p = 5 to p = 5.25. c. Use your answer to 3a to determine whether the firm’s revenue will increase or decrease if the firm raises the price? Explain you answer. dr d. Compute and use the approximation formula to estimate the change in dp p=5 the firm’s revenue if they raise the price from p = 5 to p = 5.25. 4. Compute the degree 10 Taylor polynomial of the function f (x) = ex , centered at the point x0 = 0. (This is easier than you may think at first.) √ 5. Compute the degree 2 Taylor polynomial of the function g (x) = 3 x, centered at √ the point x0 = 1000. Use this polynomial to find an approximate value for 3 1001. 6. Compute the degree 4 Taylor polynomial of the function y = ln x, centered at x = 1. Use this polynomial to compute the approximate values of ln 0.8 and ln 1.25. Note: You only need to use the Taylor polynomial once. 7. Compute the degree 2 Taylor polynomial of the function f (x) = √ x0 = 100. Use the polynomial that you found to estimate 102. √ x centered at ...
View Full Document

Ask a homework question - tutors are online