Download the App!
Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.
Question
Answered step-by-step
Use the guidelines of this section to sketch the curve.
$ y = \frac{x}{\sqrt{x^2 - 1}} $
Video Answer
Solved by verified expert
This problem has been solved!
Try Numerade free for 7 days
Like
Report
Official textbook answer
Video by Jamie M
Numerade Educator
This textbook answer is only visible when subscribed! Please subscribe to view the answer
Calculus 1 / AB
Calculus 2 / BC
Chapter 4
Applications of Differentiation
Section 5
Summary of Curve Sketching
Derivatives
Differentiation
Volume
Campbell University
University of Michigan - Ann Arbor
University of Nottingham
Boston College
Lectures
04:35
In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.
06:14
A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.
06:31
Use the guidelines of this…
20:32
15:54
14:38
So we know the graph is gonna look something like this because it's a rational function. But, um, first, let's find out the ass in totes so that we can know exactly where the graph is gonna be. First of all, the domain. Um, since there's a square on the bottom, we cannot. Well, since there's a square, yeah, we cannot have a negative under the radical. And also we cannot have the denominator to equal zero. So that means for the domain, it could be anything besides x zero so X can not equals here for the domain and ex cannot equal plus or minus one, but it can't exist anywhere else. Intercepts there are none. So substituting zero for extra Why we see that there are no intercepts. Symmetry. It's odd because F of negative X is equal to negative f of X. So it hasn't always symmetry ass until it's so first was finding vertical ascent oats. So were the denominator equal zero. We already said that was plus or minus one. So let's test out the limit as X approaches, plus or minus one. So let's do one first. Um, and if this equals infinity or negative infinity. We know it's a vertical lassitude. So substituting one, we see it's one over zero, so that's infinity. And if we do the same thing for a negative one, we just know it's gonna be negative. Infinity. So for vertical, ask himto we can say that X is plus or minus one. That's where Assam totes are, which is why the domain cannot be plus or minus one. All right, enough reverted for ah, horizontal as in two. The horizontal ask himto is where the limit approaches infinity or negative infinity. So the limit as X approaches infinity of our function X over swear ou of X squared minus one. So if we factor out in the denominator, we get the limit as X approaches Infinity of X over the square of X squared one minus one over X squared. And if we take that out of the square root. If you take this out of the square root, we get an X and X and X cancel. So we're left with the limit as X approaches. Infinity of one over the square root one minus one over X squared, won over. Affinity is zero. So one minus zero is one. So our limit is one see, and the limits as X approaches infinity or a negative infinity, we're gonna follow very similar steps. The only difference is that when we pull out because it's approaching negative infinity here. When we pull out the X squared out of the radical, we're just gonna make it negative X. So we're gonna be left with, um when they cancel out a negative on the bottom, that's the only difference. So the limit of negative square root of one minus one over X squared is negative one. So we have a horizontal ass in two. That why equals one and why equals negative one. And now we can graft with the information that we have. All right, so we're gonna put in the Assam totes and red, So here we know I should have been angry. So here we know X plus or minus one, one, minus one. That's our vertical asking totes. And we also know that why is one when why is one and negative one? We have horizontal ass in two, and that's where our function can lie. That's how you grow
View More Answers From This Book
Find Another Textbook
02:57
The National Safety Council estimates that off-the-job accidents cost U.S. b…
02:41
You've obtained a chi square of 25.32, and it's significant. You w…
02:30
One of the authors received a credit card bill for $3,470, but it included a…
03:04
You wish to test the following claim (Ha) at a significance level of α=0.10H…
02:10
The p-value for a hypothesis test turns out to be 0.05486. At a 4% level of …
01:37
You measure 23 watermelons' weights, and find they have a mean weight o…
02:08
A medical school claims that more than 28% of its students plan to go into g…
02:26
You wish to test the following claim (Ha) at a significance level of α=0.005…