To assist you in locating the appropriate continuity resources, two navigation methods are provided below. A point of discontinuity is always understood to be isolated, i. Hugh prather for problems 14, use the graph to test the function for continuity at the indicated value of x. Onesided limits and continuity alamo colleges district. It provides examples of discrete and continuous functions verbally, graphically, and in real world appl. Here is a set of practice problems to accompany the continuity. What does it mean if fx is continuous on the interval a. Calculus worksheets limits and continuity worksheets. Continuity and discontinuity 3 we say a function is continuous if its domain is an interval, and it is continuous at every point of that interval. About differentiability and continuity worksheet differentiability and continuity worksheet.
The proof is in the text, and relies on the uniform continuity of f. Worksheet 10 continuity santa ana unified school district. Examples of domains and ranges from graphs important notes about domains and ranges from graphs. Basic limit theorem for rational functions if f is a rational function, and a domf, then lim x a fx fa. In the second column, list the designated successors for each decisionmaker. These are some notes on introductory real analysis. In the first column, list key decisionmakers by position responsible for the agencys essential functions see worksheet b to determine essential functions. For each function, determine the intervals of continuity. If the function is not continuous, find the xaxis location of each. Here we are going to see some practice questions on differentiability and continuity. Remember that domain refers to the xvalues that are represented in a problem and range refers to the yvalues that are represented in a problem. If the function fails any one of the three conditions, then the function is discontinuous at x c. That is, for each function f is there a number m such that for all x, fx. The nal method, of decomposing a function into simple continuous functions, is the simplest, but requires that you have a set of basic continuous functions to start with somewhat akin to using limit rules to nd limits.
Title page, 2 page foldable, 2 page practice sheet, 3 page answer sheets the discrete and continuous foldable is a two sided foldable that can be completed by the student. Use the graph of the function fx to answer each question. The limit of a rational power of a function is that power of the limit of the function, provided the latter is a real number. The continuous function f is positive and has domain x 0. We will now take a closer look at limits and, in particular, the limits of functions. My only sure reward is in my actions and not from them. Sketch a possible graph for a function that has the stated properties.
Find the value of k that would make the function continuous in each case. Continuity of operations coop planning template and. Denition 62 continuity a function f is said to be continuous at x a if the three conditions below are satised. If g is continuous at a and f is continuous at g a, then fog is continuous at a. Example 1 determining continuity of a polynomial function discuss the continuity of each function. Worksheet 10 continuity for problems 14, use the graph to test the function for continuity at the indicated value of x.
All constant functions are also polynomial functions, and all polynomial functions are also rational functions. Determine if the following function is continuous at x 3. So, each is continuous on the entire real line, as indicated in figure 1. A function is continuous at when three conditions are satisfied. Limits of piecewisedefined functions given a piecewisedefined function that is split at some point x a, we wish to determine if lim xa fx exists and to determine if f is continuous at x a.
If this is equalled to zero and the equation is solved, the discontinuity points will be obtained. The function is continuous at r with the exception of the values that annul the denominator. The following theorem applies to all three examples thus far. For problems 3 7 using only properties 1 9 from the limit properties section, onesided limit properties if needed and the definition of continuity determine if the given function is continuous or discontinuous at the indicated points. A function f is continuous at a point x a if lim f x f a x a in other words, the function f is continuous at a if all three of the conditions below are true. A function f is continuous at x c if all three of the following conditions are satisfied. If r and s are integers, s 0, then lim xc f x r s lr s provided that lr s is a real number. Example last day we saw that if fx is a polynomial, then fis continuous. Write your answers in interval notation and draw them on the graphs of the functions.
Given a function formula or graph, be able to identify points of discontinuity explain what condition the function fails to meet at each point of discontinuity definition of continuity. Worksheet 3 7 continuity and limits macquarie university. In this section our approach to this important concept will be intuitive, concentrating on understanding what a limit is using numerical and graphical examples. This continuity resource toolkit is designed to provide partners at all levels of government, as well as the private and nonprofit sectors, with additional tools, templates and resources to assist in implementing the concepts found within the continuity guidance circular.
Then you will need to determine if the function is continuous, and, if not, how many. Worksheet 14 continuity to live for results would be to sentence myself to continuous frustration. Each of the questions in this quiz will present you with at least one function. Calculus i continuity practice problems pauls online math notes. 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. For each graph, determine where the function is discontinuous. Find the intervals on which each function is continuous. To begin with, we will look at two geometric progressions.