Question
Ifthe limr-+o f(z) = 5,then [Select ]is a Select ]asymptoteQuestion 22 ptsIfthe lim_-3+ flc) = c,the V [ Select ] Y-3 asymptote Y = infinity X= infinity X-3[Select ]
Ifthe limr-+o f(z) = 5,then [Select ] is a Select ] asymptote Question 2 2 pts Ifthe lim_-3+ flc) = c,the V [ Select ] Y-3 asymptote Y = infinity X= infinity X-3 [Select ]
Answers
Assume that $f(x)$ has domain $[0, \infty)$. Find $\lim _{x \rightarrow x} f(x)$ if the graph of $y=f(x)$ has oblique asymptote $y=\frac{1}{2} x+3$
Okay, that is time we have not. Our function has a hopefully Gaston job at y is equal turning in to expose three. So that's that mine that we have John out like So let's notice here that, um we can have a graph that look something like this. We're actually let's drawn out like this. So it's noticed that our function f of X eyes um, we increase in our values of X. We see that our wire values there are approximately this line. Here are oblique line. So we see that as X increases or why value is getting larger and larger in terms of negative numbers, that is our function. F of X is approaching negative affinity as X approaches infinity. So just here is equal to negative infinity.
Okay, we are going to find the slant ascent Tope of the rational function. So what we're going to do is we're going to divide the numerator by the denominator. So this case, since there's a single thing in the denominator, I can put each term of the numerator above the denominator, So I end up with an X -1 over X. Now, remember as far as the slain asuntos goes, that's just going to be Y equals X. That extra minus one over X squared will approach zero as X goes to infinity or negative infinity.
Were given the rational function shown, and were asked what the slant ascent taub is now having. A single term on the bottom means that we can set each of the terms on top, and we can divide by the X. So we have the 4000 divided by X 20 divided by X, which is 20 And then .0001 X. Because the X squared divided by X is X. So the slant ascent tope is our X term plus 20.
All right. So for problems, 7 47 were given this function. And we need to find this slant Assen took. So before we do that, we needs toe. We need to first check if it actually house so slammed, asking tough. So a function will have a slant ascent of if the degree or the highest exponents of the numerator is a larger than the degree of the denominator. So the highest exponents of the numerator is too, and the highest of exponents of the denominator is one. So the degree of the numerator is larger than the degree of the denominator, which means there is going to be a slight at symptoms. And now, to find that slant hasn't though There are two ways you basically just to divide the numerator by the denominator. And like I said, there are two ways to do the long division or it's intact division. So first we will use the long division. So you take the divisor X minus one. You make a division bracket thus was called and then you put the dividend inside the practice, so X squared plus three X minus threes. Now you do the divine ing So what do you have to multiply? X minus one? Who is so that the leading term will gain X squared? Well, it's just act since next time. Sexist X squared. So excellent access Xcor. That's what you just mentioned. And then x times None of the oneness minus acts. So now he's attract X Square is cancel out. And then there's the three x minus negative X, which is basically plus X 24 acts. And then we bring down the next term, which isn't like the three. And then we continue. So would you have to multiply X minds one so that the leading term ist for X? Well, it's just for so we add plus four to their questions. So four times access for acts four times negative one is 94 so minus four when there was attracts. So the four X's cancel out and negative three of minus negative for or post for us Just one. And just like that, where you found are slant aspecto, which is why is he calls an X Plus four and the remainder than we got this one here really doesn't matter, so we can just completely ignorant and now for a synthetic division. So first we have toe find out like, what's the format of the divisor for us in tech division? Well, the binomial has the divisor Horton since Activision. This written in the form of X minus C. We're seeing a constant number. So our device, or here is X minus one, which means that see, it's gonna be positive one. So with that, we take this number one and we draw like a corner here to separate it from the other numbers. And then we write down the coefficients of each term such that the exponents are decreasing. So it's the excess squared and an axe and then no x. So it's already in the decreasing order, exponents wise. So we can imagine this. That's one times X squared in the front. So it's gonna be one positive three and the nectar three. So one. Sorry. Sorry. So it's game time lagging here. Sorry, three and then number three and then we draw a line and then we bring this first numbers out. So everyone here and then we multiplying this number by the number in the upper left. So one time, someone that salon you bring it back up the line here and then we adds with a number of us, so three plus one is four, and then the cycle repeats so four times one, those four would bring it back up. And then we added, with the number of both so negative three plus Flores one. And just like that, we found the quotient for when you divide this dividend by X minus one. So the question is gonna geo tax plus more with the one that's the remainder. But like I said, it doesn't matter for the sign asking toe. And just like that, we've confirmed that the slant essence of IHS why Sequels and expose for