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Find the limit or show that it does not exist.

$ \displaystyle \lim_{x \to \infty}\frac{x + 3x^2}{4x - 1} $

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Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 6

Limits at Infinity: Horizontal Asymptotes

Limits

Derivatives

Missouri State University

Campbell University

Oregon State University

University of Michigan - Ann Arbor

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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Find the limit or show tha…

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This is a problem. Number 26 of the Super Calculus eighth edition section 2.6. Find the limit or show that it does not exist. The limit as experts is infinity X plus three X squared, divided by quantity four X minus one. And what we're going to, uh, look to use is that limit as experts. Infinity of a. An expression of the form, one of our extra R where R is a rational value. Graded zero. Islam is equal to zero. If we were to help produced this limit into forms of this definition to our advantage, it will be divided by X in the numerator and the denominator. Our first term is X or X is one plus three x squared over excess three X and the denominator. We will get for extra by excess for minus one over X is one or X. Now we use our properties limits, which allow us to take the LTD each of these terms individually. And then we used the definition and we know that this term approaches zero as X approaches infinity a mistake. Islam. It is the same as the original experts infinity. And so there's one of Rex term approach Jazeera. As exporters affinity the numerator we can see approaches three times infinity. So the numerator will actually be approaching infinity in this case, since it gets bigger without bound numerator, denominator remains at 40 approximately. But this is the same as positive. Infinity, as for, is much smaller than infinity. So what we say is that this limit does exist and it's an infinite limit equal to infinity. Positive infinity.

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