Differentiation rules

Multivariable calculus

Marginal rate of substitution

Functions and mappings

Second derivative

Factorization

Running head: DECISION-MAKING IN AGRIBUSINESS 1 DECISION-MAKING IN AGRIBUSINESS 8 Decision-Making in Agribusiness: Quantitative Applications (AGSC5300) Name Institution Decision-Making in Agribusiness: Quantitative Applications (AGSC5300) Problem 1 To differentiate the function, Y=?lnX?, the chain rule is applied. Fundamentally, the rule states that, for a function of the form Y=f(f(X)) the derivative is computed as follows: First, let f(X) be a value, say U. The function may therefore be written as Y=f(U) Then, the function is differentiated with respect to U That is, Next, the derivative of U with respect to X is calculated That is, Combining the above two derivatives gives the chain rule: =* Applying the above rule, let X? be U Therefore, Y=?lnU.

ap calculus

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Rahn ? 2008 AP Calculus ? Final Review Sheet When you see the words ?. This is what you think of doing 1. Find the zeros of a function. Set the function equal to zero and solve for x. 2. Find equation of the line tangent to f(x) at (a,f(a)). Find f ?(x),the derivative of f(x). Evaluate f ?(a). Use the point and the slope to write the equation: y= f ?(a)(x-a)+f(a) 3. Find equation of the line normal to f(x) at (a,f(a)). Find f ?(x),the derivative of f(x). Evaluate f ?(a). The slope of the normal line is 1 '( )f a ? . Use the point and the slope to write the equation: ( ) ( ) ( ) 1 y x a f a f ? a = ? + 4. Show that f(x) is even. Evaluate f at x = -a and x = a and show they are equal.

AP Calc Study Guide

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Integration by substitution

Integral calculus

Integration by parts

Differential equation

education

Copyright 1996,1997 Elaine Cheong All Rights Reserved Study Guide for the Advanced Placement Calculus AB Examination By Elaine Cheong 1 Table of Contents INTRODUCTION 2 TOPICS TO STUDY 3 ? Elementary Functions 3 ? Limits 5 ? Differential Calculus 7 ? Integral Calculus 12 SOME USEFUL FORMULAS 16 CALCULATOR TIPS AND PROGRAMS 17 BOOK REVIEW OF AVAILABLE STUDY GUIDES 19 ACKNOWLEDGEMENTS 19 2 Introduction Advanced Placement1 is a program of college-level courses and examinations that gives high school students the opportunity to receive advanced placement and/or credit in college. The Advanced Placement Calculus AB Exam tests students on introductory differential and integral calculus, covering a full-year college mathematics course.

AP Calculus Cheat Sheet

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Integral calculus

Integration by substitution

Integration by parts

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Quotient Rule

Antiderivative

Product rule

Calculus Cheat Sheet Visit http://tutorial.math.lamar.edu for a complete set of Calculus notes. ? 2005 Paul Dawkins Limits Definitions Precise Definition : We say ( )limx a f x L? = if for every 0e > there is a 0d > such that whenever 0 x a d< - < then ( )f x L e- < . ?Working? Definition : We say ( )limx a f x L? = if we can make ( )f x as close to L as we want by taking x sufficiently close to a (on either side of a) without letting x a= . Right hand limit : ( )limx a f x L+? = . This has the same definition as the limit except it requires x a> . Left hand limit : ( )limx a f x L-? = . This has the same definition as the limit except it requires x a< . Limit at Infinity : We say ( )limx f x L?? = if we

Ch9 SG

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Ordinary differential equations

Functions and mappings

Integral calculus

Differential equation

Derivative

Differential of a function

Multiple integral

Order of integration

Law

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Ordinary differential equations