In this lecture, we work out each example only by looking at the graph. The best way for us to understand what limits really are is to look at a bunch of different examples which exhibit different types of behaviors around x=c for some fixed value c. Later we will come back and define this concept more formally. There are more formal definitions of continuity, but we use this one for now because it is easy to understand intuitively. Throughout this lecture, we will often use the word discontinuity, so we define it (at least informally, for now) here:Ĭontinuous, Discontinuity (informal definition)Ī function is continuous in an interval if the graph of that function over that interval can be drawn in one stroke (without lifting your pen from the paper).Ī discontinuity on a graph is any point at which the graph is NOT continuous (e.g. But before we do that, we briefly introduce a definition that we will use in the examples that follow. The best way for us to better understand what a limit is, is just to jump in and start looking at different functions and discussing what the limit might be for specific x-values for that function. Once we have developed a more intuitive feel for what limits really are, we will come back and formally define these terms. This definition is informal because we haven't formally defined what we mean by "approaches" or "eventually gets closer and closer". Lim x → 2+ f(x) = L means that the limit of f(x) as x approaches 2 from the right is L Lim x → 2- f(x) = L means that the limit of f(x) as x approaches 2 from the left is L and Lim x → -2+ f(x) = L means that the limit of f(x) as x approaches -2 from the right is L Lim x → -2- f(x) = L means that the limit of f(x) as x approaches -2 from the left is L Lim x → c f(x) = L to denote "the limit of f(x) as x approaches c is L"īe careful!: The plus or minus sign which appears after the c denotes the direction from which x approaches c - it does NOT mean that c itself is positive or negative (it may be either)! Lim x → c+ f(x) = L to denote "the limit of f(x) as x approaches c from the right is L" Lim x → c- f(x) = L to denote "the limit of f(x) as x approaches c from the left is L" If f(x) has different right and left limits, then the two-sided limit ( lim x → c f(x)) does not exist.) (If f(x) never approaches a specific finite value as x approaches c, then we say that the limit does not exist. If the limit of f(x) as x approaches c is the same from both the right and the left, then we say that the limit of f(x) as x approaches c is L. If f(x) eventually gets closer and closer to a specific value L as x approaches a chosen value c from the left, then we say that the limit of f(x) as x approaches c from the left is L. Please see the TI-83 Plus and TI-84 Plus Family guidebooks for additional information.If f(x) eventually gets closer and closer to a specific value L as x approaches a chosen value c from the right, then we say that the limit of f(x) as x approaches c from the right is L. This will give us the limit as X approaches 3, which is equal to 2. Using the example (x+1)/(x-1) let us find the limit as X approaches 3:Ģ) Press ģ) Press to select 6:Zstandard and set default window settings.Ĥ) Press then to change the Xmin and Xmax.Ħ) Press to start the table near 3 and press to set the table step.ħ) Press followed by to display the table.Ĩ) Looking at the numbers in the table as x approaches 3. While there is no built in function that can easily find the limits on the calculator, there is a work around. How can I find the limits on the TI-83 Plus and TI-84 Plus family of graphing calculators? Solution 34619: Finding the Limit of a Function on the TI-83 Plus and TI-84 Plus Family of Graphing Calculators.
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