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Explain in your own words the meaning of each of the following.
(a) $ \displaystyle \lim_{x \to \infty} f(x) = 5 $(b) $ \displaystyle \lim_{x \to - \infty} f(x) = 3 $
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01:19
Daniel Jaimes
Calculus 1 / AB
Chapter 2
Limits and Derivatives
Section 6
Limits at Infinity: Horizontal Asymptotes
Limits
Derivatives
Pio H.
February 22, 2021
Can the graph of y=f(x) intersect a vertical asymptote? can it intersect a horizontal asymptote? illustrate by sketching graphs.
Missouri State 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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for this problem, we are to explain the meaning of each of the following statement. The first one is the limit of F of X as X approaches infinity equals five, and The other one is the limit of the function. As X approaches negative infinity equals three. Now, for the first one, since X approaches infinity, then it tells us that we are moving far to the right and we're looking at the value the function varied approaches to and since this is equal to five, then as we move far right, the value of the function approaches to five. Because X approaches an infinite value, The value of F of X can never equal five. It will only approach it. And so we can say that the function Has a horizontal sm so that y equal to five. Now for the 2nd 1, since we're approaching negative infinity, then we're moving far to the left. And so as you move far to the left, the value of the function approaches 23 And because X approaches negative infinity, Then the value of F of X can never equal to three. It will only approach it. Hence we can say that F of X has a horizontal essent. Oh, dad, Why equal to 3?
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