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# Evaluate the limit, if it exists.$\displaystyle \lim_{x \to 5}\frac{x^2 - 6x + 5}{x - 5}$

## 4

Limits

Derivatives

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

So here we have a specific limit. The limit as X approaches five of x squared minus six. X plus five Divided by X -5. So the first thing we can check if this is an indeterminate form and we can evaluate the limit. So 5 -5 is zero. And this we can also find is also equivalent. 20. So as a result we have an indeterminate form and we can value to limit. So one thing we can do is first to factor the numerator. So this would be X -5 Times X -1 Over X -5. So we can cross out the X -5 to simplify down our expression and we have this remaining. So if we can use direct substitution here, since we don't have an indeterminate form And we find that this is equivalent to four. An alternative way of doing this would be applying logical rule. So applying law in the world would also give us uh the same answer. However, a lot the world would require a bit more work as we have to differentiate the numerator and denominator. And but this gives our final answer and the limits equivalent to four

Johns Hopkins University

#### Topics

Limits

Derivatives

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp