Inverse functions calculus pdf notes

Figure 1 inverse functions are symmetric about the line y x. Hyperbolic trigonometric functions, the fundamental theorem of calculus, the area problem or the definite integral, the antiderivative, optimization, lhopitals rule, curve sketching, first and second derivative tests, the mean value theorem, extreme values of a function, linearization and differentials, inverse. Ive tried to make these notes as self contained as possible and so all the information needed to read through them is either from an algebra or trig class or contained in other sections of the notes. If has an inverse function, then is differentiable at any for which. Calculus ii mat 146 derivatives and integrals involving inverse trig functions as part of a first course in calculus, you may or may not have learned about derivatives and integrals of inverse trigonometric functions. You appear to be on a device with a narrow screen width i. All the inverse trigonometric functions have derivatives, which are summarized as follows. To determine whether the inverse is a function switch x and y values and determine whether the domain of inverse is paired with only one value in the range domain can not repeat inverse. For every pair of such functions, the derivatives f and g have a special relationship. Here are my online notes for my calculus i course that i teach here at lamar. It was developed in the 17th century to study four major classes of scienti. Be sure to get the pdf files if you want to print them. Derivatives of inverse trig functions here we will look at the derivatives of. A function must be onetoone any horizontal line intersects it at most once in order to have an inverse function.

Recall the following definitions of relations and functions. Slope of the line tangent to at is the reciprocal of the slope of at. Pdf produced by some word processors for output purposes only. Finding angles using given sides and inverse trigonometric functions. Find materials for this course in the pages linked along the left. We would like to create an inverse function with domain y that maps back to x.

This book is a revised and expanded version of the lecture notes for basic calculus and other similar courses. There are videos pencasts for some of the sections. Each of the six basic trigonometric functions have corresponding inverse functions when appropriate restrictions are placed on the domain of the original functions. In order for both a function fx and its inverse fx 1 to. In what follows, we discuss the behavior and graphs of these functions and give examples of situations appropriately modeled by such functions. Derivatives of inverse functions video khan academy. Math 221 1st semester calculus lecture notes version 2. Calculus i inverse functions pauls online math notes. If x,y is a point on the graph of the original function, then y,x is.

Microsoft word 17 guided notes te inverse relations and functions. The function obtained in this way is called the inverse of f. Battaly, westchester community college, ny homework part 1 homework part 2. Math 221 first semester calculus fall 2009 typeset. Due to the nature of the mathematics on this site it is best views. As usual, standard calculus texts should be consulted for additional applications. These appear to be inverse functions, but what about x0. I havent written up notes on all the topics in my calculus courses, and some of these notes are incomplete they may contain just a few examples, with little exposition and few proofs. Learn about this relationship and see how it applies to and lnx which are inverse functions. In the textbook by stewart, precalculus, mathematics for calculus, 6th ed. We simply use the reflection property of inverse function. Inverse functions onetoone functions a function f is. Emphasize the relationship between the domain and range of a onetoone function and its inverse. Calculus ii mat 146 derivatives and integrals involving.

Your ap calculus students will apply the properties of inverse functions to the derivatives of inverse functions and apply rules for bases and logarithms to find derivatives of exponential and logarithmic functions. The notes were written by sigurd angenent, starting. Inverse functions are just a reflection across the line y x. Calculus i or needing a refresher in some of the early topics in calculus. If we know the derivative of f, then we can nd the derivative of f 1 as follows. For the love of physics walter lewin may 16, 2011 duration. In this section we will define an inverse function and the notation used for inverse functions. Understanding basic calculus graduate school of mathematics. Derivative of the inverse function at a point is the reciprocal of the derivative of the function at the corresponding point. These notes are being written for an introductory honors calculus class, math. Calculus 1 class notes, thomas calculus, early transcendentals, 12th edition copies of the classnotes are on the internet in pdf format as given below. Here are the steps required to find the inverse function.

Make sure that students understand the difference between y and x as notated in y fx and y f1 x finding inverses of quadratic and rational functions is a good exercise. Derivatives of inverse function problems and solutions. We describe the notion of the inverse of a function, and how such a thing can be differentiated, if f acting on argument x has value y, the inverse of f, acting on argument y has the value x. The would like to denote the additive inverse of a, as customary, a. Inverse functions mctyinverse20091 an inverse function is a second function which undoes the work of the. Domains are restricted to make them functions so do not worry about sin versus sin. The graph of an inverse function is the reflection of the original function about the line y x. Accompanying the pdf file of this book is a set of mathematica. Watch the video lecture differentiation of inverse functions. Lecture notes single variable calculus mathematics. This is a self contained set of lecture notes for math 221.