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Solving Easy Limits

There are two types of easy limit problems: the ones you should just memorize and the ones where you can plug in the x-number and get the answer in one step.

Limits to memorize

You should memorize the following limits to avoid wasting time trying to figure them out. (Pay special attention to the last three limits.)

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(y = c is a horizontal line, so the limit — which is the function height — must equal c, regardless of the x-number.)

image1.png

Plugging and chugging

You can use the plug-and-chug method to solve some limit problems. Just plug the x-number into the limit function, and if the computation results in a number, that’s your answer (don’t forget that zero divided by anything other than zero equals zero which is, of course, a number). For example

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This method always works for limits that involve continuous functions and functions that are continuous over their entire domains. These are well-duh limit problems, and, to be perfectly frank, there is really no point to them. The limit is simply the function value.

The plug-and-chug method also works for any other type of function, including piecewise functions, unless there is a discontinuity at the x-number you plug in. (A piecewise function has separate pieces, where each part of the piecewise function has its own equation.)

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