To prove a limit doesnt exist, find two paths to a,b that give different limit values. This section contains lecture video excerpts, lecture notes, a worked example, a problem solving video, and an interactive mathlet with supporting documents. Lecture notes in calculus pdf 206p this is useful notes for calculus. As fwill take di erent values for di erent xed values of, the limit at the origin does not exist.
Benginning calculus lecture notes 2 limits and continuity. A function is a rule of correspondence that associates with each object x in one set called the domain, a single value. Partial derivatives if fx,y is a function of two variables, then. Updated lecture notes include some new material and many more exercises. We will also see the mean value theorem in this section. Calculus 1 class notes, thomas calculus, early transcendentals, 12th edition copies of the classnotes are on the internet in pdf format as given below. This lecture describes the mathematical notion of continuity, and then illustrates these. Lecture notes single variable calculus mathematics.
Limits and continuity this table shows values of fx, y. This section contains lecture video excerpts, lecture notes, a worked example, a problem solving video, and an interactive mathlet. We say that the limit of fx as x tends to c is l and write lim xc fx l provided that roughly speaking as x approaches c, fx approaches l or somewhat more precisely provided that fx is closed to l for all x 6 c, which are close to. The concept of limit, computation of limit, continuity and its consequences, limits involving infinity, tangent lines and velocity, computation of derivatives, derivatives of. Cm111a calculus i compact lecture notes acc coolen department of mathematics, kings college london version of sept 2011. If c is an accumulation point of x, then f has a limit at c. A more recent version of this course, taught by prof. The lecture notes for this course are courtesy of brenda ng, a student in the class. Note that as x goes to negative infinity we obtain the same limit. Be sure to get the pdf files if you want to print them. C is a rule that assigns unique complex number, denoted by fz to every number z2s. The real number lis called the limit of the sequence tanu. Continuity in this section we will introduce the concept of continuity and how it relates to limits. This is a self contained set of lecture notes for math 221.
Continuity of a function at a point and on an interval will be defined using limits. Understand the concept of and notation for a limit of a rational function at a point in its domain, and understand that limits are local. If you expect the limit does exist, use one of these paths to. Limits will be formally defined near the end of the chapter. The value of the function at the point coincides with the limit of the function at the point.
Twosided limit lim xc f x f xhas a limit as x approaches c if and only if the right and left hand limits at c. These are some lecture notes for the calculus i course. Ap calculus limits, continuity, and differentiability. It is hoped however that they will minimize the amount of note taking activity which occupies so much of a students class time in most courses in mathmatics.
As is often the case, you might not know how to draw the graph until later. The latex and python les which were used to produce these notes are available at the following web site. They cover the properties of the real numbers, sequences and series of real numbers, limits of functions, continuity, di erentiability, sequences and series of functions, and riemann integration. And if you begin a lecture having understood the previous one. Pdf in this expository, we obtain the standard limits and discuss continuity. In order to further investigate the relationship between continuity and uniform continuity, we need. Limits and continuity a guide for teachers years 1112. Lecture notes in calculus raz kupferman institute of mathematics the hebrew university july 10, 20. This is the limit, and it has its own notation as you will see the limit is a notion of motion example 3. Lecture notes for analysis ii ma1 university of warwick. Lecture notes theory of probability mathematics mit. 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. Pdf limit and continuity revisited via convergence researchgate. Few students understand everything during the lecture.
Continuity and limits contents 1 introduction to citeseerx limits and continuity questions and answers pdf,solved examples of limits and continuity,calculus limits and continuity pdf,limit exercises and answers pdf,limits and continuity formulas pdf,limits of functions pdf,limits solved problems pdf,limit and continuity notes, limits and continuity examples,limits continuity and. The next theorem proves the connection between uniform continuity and limit. View notes lecture 12 limits and continuity of trigonometric functions. Functions of several variables and partial di erentiation. Advanced calculus lecture notes for mathematics download. The notes were written by sigurd angenent, starting from an extensive collection of notes and problems compiled by joel robbin. There are videos pencasts for some of the sections. Benginning calculus lecture notes 2 limits and continuity 1.
The definition of the limit we will give the exact definition of several of the limits covered in this section. There is plentiful evidence that putting in this e. Continuity of functions in vector calculus is pretty much the same as for calculus i, with a bit of extra structure. Then, we say f has a limit l at c and write limxc fx l, if for any.
Lecture note functions, limit and continuity of function. R, and let c be an accumulation point of the domain x. Functions of several variables and partial differentiation 2 the simplest paths to try when you suspect a limit does not exist are below. This notes contain real numbers, functions, derivatives, integration theory and sequences.
Intuitively, a function is continuous if you can draw its graph without picking up your pencil. In what follows, i will freely invoke various technical terms such as limit, continuity, derivative, etc, pertinent to differential calculus. This session discusses limits and introduces the related concept of continuity. Limits, continuity, and differentiability student sessionpresenter notes this session includes a reference sheet at the back of the packet since for most students it has been some time since they have studied limits. We say that the limit of fx as x tends to c is l and write lim xc fx l provided that roughly speaking as x approaches c, fx approaches l or somewhat more precisely provided that fx is closed to l for all x 6 c, which are close to c. Ma 1 lecture notes continuity consider the following graph of the function fx. The cost at the gas station depends on the number of gallons of gas you pumped into your car. Calculus2 formulaesheet exam sem 1, 20 questions and answers. Shortly after each lecture, spend an hour going over lecture notes and working on the assignments. It is called partial derivative of f with respect to x. We say the limit of fx as x approaches a is l, denoted lim x. These are some notes on introductory real analysis.
In mathematics we often describe one quantity in terms of another. Continuity of the algebraic combinations of functions if f and g are both continuous at x a and c is any constant, then each of the. It was developed in the 17th century to study four major classes of scienti. Beginning calculus limits and continuity shahrizal shamsuddin norashiqin mohd idrus department of mathematics, fsmt upsi lecture slides series villarino domath, fsmtupsi d1 limits and continuity 1 54 2. The amount of your paycheck if you are paid hourly depends on the number of hours you worked.
Pdf produced by some word processors for output purposes only. These are introduced and discussed in detail in various. Paper 4 fundamentals of business mathematics and statistics the institute of cost accountants of india cma bhawan, 12, sudder street, kolkata. It deals with fundamental limits first and the rules of differentiation for all the elementary functions.
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