P29 - Project 29 MAC 2311 YOU MUST SHOW YOUR WORK TO...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

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

Unformatted text preview: Project 29 MAC 2311 YOU MUST SHOW YOUR WORK TO RECEIVE FULL CREDIT!! 1. In Lecture 23 we saw that Mean Value Theorem can be used to prove the following: If f and g are two functions such that f ( x ) = g ( x ) on an interval ( a, b ), then there is a constant C such that f ( x ) = g ( x )+ C for all x in ( a, b ) . How does this explain our formula for the general antiderivative of a function (that is, if F is an antiderivative of f , why must all others be F plus a constant)? You can use this property to prove interesting identities. For example. . . Look at the functions y = tan 2 ( x ) and y = sec 2 ( x ) . Show that they have the same derivative. What then must be the relationship between the two functions? Use this relationship to prove the identity tan 2 ( x ) + 1 = sec 2 ( x ) . Look at the function y = x 1 ln( x ) . Calculate the derivative using logarithmic differentiation. (Does the answer surprise you?) What other functions have this derivative?...
View Full Document

This note was uploaded on 01/13/2010 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

Page1 / 2

P29 - Project 29 MAC 2311 YOU MUST SHOW YOUR WORK TO...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online