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Find the limit, if it exists. If the limit does not exist, explain why.

$ \displaystyle \lim_{x \to 0^+}\left(\frac{1}{x} - \frac{1}{|x|} \right) $

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Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 3

Calculating Limits Using the Limit Laws

Limits

Derivatives

Missouri State University

Campbell University

Oregon State University

Harvey Mudd College

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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is problem number forty six of this tour Tactless eighth edition section two point three Find the limited It exists. There's a limit does not exist. Explain away the limit is expert zero from the right of the quantity one over X minus one over the absolute value picks. We notice that as experts zero, each of these terms is indeterminant. So our approach is to combine the two factions and cft functions and defines in any way we haven't upset value function here. Ah, that we first I need to deal with before we can try to combine the two fractions on what we know about the absence of Value X is that it is the same as just a God you x are the function X when X is greater than or equal to zero and it's equivalent to negative X when X is less than zero for this limit, though, however, we are only concerned with ex approaching zero from the right. This guarantees that the values of X are positive and or equal to zero. And so our absolute value function reduces too absolutely of X rays to just x pretties for for the for the reason that we're putting serve from the right and that the function itself is just the same as X in this region. Now we can see that we can simplify this limit pretty easily. One over X minus on a rex gives us zero. And the limit is you're prettier from the right of dysfunction. Zero gives us the upper limit from the right is equal to zero.

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