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Unit 1

# 1.4 Estimating Limit Values from Tables

Anusha Tekumulla

### AP Calculus AB/BCΒ βΎοΈ

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Using tables to estimate limit values helps us better visualize what a limit actually is. In order to understand this concept, letβs look at an example.Β π­

## Example Problem β

The easiest way to find a limit is to plug in the given x value into the function. However, youβll find that the given function isnβt defined at x = 3 because the denominator evaluates to 0. Because we canβt find the function value at x = 3, we find the limit by approaching x = 3.Β
1) We have to make a table and the first step is picking the x values to use. Pick a value that's a little bit less than x = 3 (that is, a value that's "to the left" π of 3), so maybe start with something like x = 2.9.
 x 2.9 3 f(x) 0.16949 undefined
2) Next, add a couple more x-values to your table to simulate the feeling of getting infinitely close to x = 3, from the left.
 x 2.9 2.99 2.999 3 f(x) 0.16949 0.16694 0.16669 undefined
3) Approach x = 3 from the right just like we did from the left.Β
 x 2.9 2.99 2.999 3 3.001 3.01 3.1 f(x) 0.16949 0.16694 0.16669 undefined 0.16664 0.16639 0.16393
Now that we have our table, we can estimate the limit of f(x) = x - 3 β x^2 - 9 at x = 3 is 0.1667 or 1 β 6.Β
It is important to pick x values that get infinitely close to the target value. In the example above, we picked numbers that were closer and closer to x = 3. We wouldnβt be able to estimate the limit value if we used numbers with equal increments like 2.25, 2.5, and 2.75.Β

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