Limits Analytically. Find the limit of Steps to Solve for Limits 1) Substitute the value in 2) Factor and Cancel (maybe rationalize) 3) The answer is.

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Presentation transcript:

Limits Analytically

Find the limit of

Steps to Solve for Limits 1) Substitute the value in 2) Factor and Cancel (maybe rationalize) 3) The answer is either, or DNE. Here you need to plug in values to the left and right like you’re graphing the problem.

Let’s look at some of the common graphs you might see in the calculus class to see what you might encounter while doing limits super easy limits (no asymptotes or holes) they’re continuous y=mx+b

Find

pretty easy: Holes, where the denominator cancels with a factor of the numerator

Find

most difficult: asymptotes, you have a denominator and it doesn’t cancel out

Find Check from the left and the right