We have now examined functions of more than one variable and seen how to graph them. In this section, we see how to take the limit of a. Tutorial which is an introduction to limits from a numerical point of view. A LiveMath Notebook on exploring continuity of a piecewise defined function. to mean that f(x) approaches the number L as x approaches (but is not equal to) a from both sides. A more precise way of phrasing the definition is that we can. Author: Doug Schoen Country: Tuvalu Language: English Genre: Education Published: 22 November 2014 Pages: 93 PDF File Size: 42.64 Mb ePub File Size: 1.27 Mb ISBN: 255-1-17529-373-6 Downloads: 34963 Price: Free Uploader: Doug Schoen Limits and continuity surface is shown in figure Fortunately, the functions we will examine will typically be continuous almost everywhere. Usually this follows easily from the fact that closely related functions of one variable are continuous. A Javascript exploration in getting numerical evidence for determining an infinite limit. Computer programs which will generate numerical evidence for determining a limit.

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• Limits and Continuity

Remember that factors that can be removed result in removable discontinuities, or holes. These are the two limits to learn: Removable discontinuities are those where there is a hole in the graph as there is in this limits and continuity.

A function is continuous on an interval if we can draw the graph from start to finish without ever once picking up our pencil.

The graph in the last example has only two discontinuities since there are only two limits and continuity where we would have to pick up our pencil in sketching it.

In other words, a function is continuous if its graph has no holes or breaks in it.

Calculus I - Continuity

Example 2 Determine where limits and continuity function below is not continuous. So all that we need to is determine where the denominator is zero.

A nice consequence of continuity is the following fact. With this fact we can now do limits like the following example. Example 3 Evaluate the following limit. 