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Find the limit or show that it does not exist.
$ \displaystyle \lim_{x \to -\infty}\frac{4x^3 + 6x^2 - 2}{2x^3 - 4x + 5} $
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03:28
Daniel Jaimes
Calculus 1 / AB
Chapter 2
Limits and Derivatives
Section 6
Limits at Infinity: Horizontal Asymptotes
Limits
Derivatives
University of Michigan - Ann Arbor
University of Nottingham
Idaho State University
Boston 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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Find the limit, if it exis…
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To evaluate this limit me 1st factor out the variable with the highest exponent for the numerator and variable with the highest exponent for the denominator. That means we have limit as X approaches infinity of in this case the numerator well have X cubed as its variable with the highest exponent. And so we get X cubed times. We have four plus six over X two over X cube. And then this will be divided by um for the nominator. We also have X cube as the variable with the highest exponents. So we have X cubed times two minus, pour over X squared plus five over X to the 3rd power. Now simplifying this, we can cancel out the X cube and we have the limit as X approaches infinity of four plus six over x -2 over X. Cube. That's divided by 2 -4, x squared Plus five over x cubed. Now evaluating at infinity we have four plus six over infinity -2 over infinity over 2 -4 over infinity plus five over infinity. Now Know that a constant over infinity will always approach zero. And so six over infinity will approach zero as well as to over infinity for over infinity and five over infinity. And so we are left with 4/2 which reduces to two. And so this is the value of the limits
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