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Find the limit or show that it does not exist.
$ \displaystyle \lim_{x \to -\infty} \frac{1 + x^6}{x^4 + 1} $
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Calculus 1 / AB
Chapter 2
Limits and Derivatives
Section 6
Limits at Infinity: Horizontal Asymptotes
Limits
Derivatives
Campbell University
Oregon State University
Harvey Mudd College
Idaho State University
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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This is problem number thirty four of the Stewart character. The Safe Edition Section two point six. Find the limit or show, but it does not exist. The Ltd's expertise. Negative infinity. I want those extra sixth over X to the force of plus one s o. One thing Khun do is we can make a choice defending the numerator and the denominator by exit the fourth and in this case, choosing anything greater than except forthe, such as Exit six. Ah, well, not benefit us since it will make the dominator a purse era. So the choice effects of the fourth should work well. Numerator becomes one of Rex to the fourth plys X squared. Since that is extra sixty minute makes in the fourth continuing to do any extra forth and the new denominator yet one plus one of Rex of the Force Ah, as we know a pro as we approach negative infinity, Each of these terms won a race for the fourth vanishes The approach Ciro and what were left over with is X squared over one. And as we approach negative infinity X squared approaches positive infinity. So this functioned averages does not the limit is that exists as thie limited approaching positive infinity as experts native
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