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# Find the limit or show that it does not exist.$\displaystyle \lim_{x \to \infty}\frac{x + 3x^2}{4x - 1}$

## $\infty$

Limits

Derivatives

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

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.

#### Topics

Limits

Derivatives

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp