Limits That Fail to Exist Identify three types of behavior associated with the nonexistence of a limit.Illustrate each type with a graph of a function.

Formal Definition of Limit Given the limit

$\lim _{x \rightarrow 2}(2 x+1)=5$use a sketch to show the meaning of the phrase$$" 0<|x-2|<0.25$ implies $|(2 x+1)-5|<0.5"$$

Functions and Limits Is the limit of $f(x)$ as $x$ approaches calways equal to $f(c) ?$ Why or why not?

Estimating a Limit Numerically In Exercises$5-10$ , complete the table and use the result toestimate the limit. Use a graphing utility to graphthe function to confirm your result.

$$\lim _{x \rightarrow 4} \frac{x-4}{x^{2}-5 x+4}$$

Estimating a Limit Numerically In Exercises $5-10$ , complete the table and use the result toestimate the limit. Use a graphing utility to graph the function to confirm your result.

$$\lim _{x \rightarrow 3} \frac{x-3}{x^{2}-9}$$

Describing Notation Write a brief description of the meaning of the notation $\lim _{x \rightarrow 8} f(x)=25$

See The Answer

Okay, So this expression means that the function of X and two 25 as 10 to 8. So if you look in a grass and we have some random function, but eight way have the 0.25 so we can have random function and it approaches 25 at actually ate on both sides.

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## Discussion

## Video Transcript

Okay, So this expression means that the function of X and two 25 as 10 to 8. So if you look in a grass and we have some random function, but eight way have the 0.25 so we can have random function and it approaches 25 at actually ate on both sides.

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