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Evaluate the limit, if it exists.
$ \displaystyle \lim_{x \to 5}\frac{x^2 - 6x + 5}{x - 5} $
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02:09
Daniel Jaimes
Calculus 1 / AB
Chapter 2
Limits and Derivatives
Section 3
Calculating Limits Using the Limit Laws
Limits
Derivatives
Missouri State University
Harvey Mudd College
Idaho State University
Lectures
04:40
In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.
In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.
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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
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