Finding the limit graphically Limits may not exist: • if the values near x = a cannot 'agree' on a common y-value, the limit might not exist • consider approaching along f from the left • and then consider approaching from the right • do our two approaches "come together"? if they come together, then we say the limit equals the matching output as we approach from each side • if they do not come together, we say the limit "does not exist" (DNE) Practice Graph A Graph B 1.0 1,0 1,0 lim f(x) = lim f(x) = x-1 x-1 Graph C Graph D

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Q: -2 if x 2

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.