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Evaluate the limit, if it exists.

$ \displaystyle \lim_{x \to 3}\frac{\frac{1}{x}-\frac{1}{3}}{x - 3} $

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02:06

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

Baylor University

University of Nottingham

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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Evaluate the limit, if it …

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Find the limit (if it exis…

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Evaluate the indicated lim…

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Find the limit.$$\…

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So here we have a specific limit. We have the limit as X purchased three of one divided by x -1 3rd over X -3. So you can evaluate this by one of the simpler techniques we have, which would be multiplying the numerator and denominator by three X. Otherwise essentially we have an indeterminate form with zero in the numerator and zero in the denominator. So We can find that this is equivalent to the limit as X approaches three of 3 -1 Divided by three x times x -3. So one thing we can do here is take the uh bring a negative out in the numerator negative x minus three, Divided by three x times x -3. So we can cross our X -3. And this would be equivalent to the limit as X approaches three of negative one divided by three X. And we can now use direct substitution since we don't have our indeterminant form anymore. And this would be equivalent to -1 knife. Another way to value this should be by using a lot lower overall where we differentiate the numerator and differentiate the denominator. But in this case likely it would be more simple by just using our standard limit techniques. And this is our final answer

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