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Instructor 3 have Prevlew Mv 32 unlimited overall recorded score I Enter attempts this-problem furction as your remaining 0%. times Submit Answers answer ]Use part ...

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Instructor 3 have Prevlew Mv 32 unlimited overall recorded score I Enter attempts this-problem furction as your remaining 0%. times Submit Answers answer ]Use part / Tdu 1 4: Probiem List Thealcin Problem Next Calculus#NIRAUODf(c) = 87 1

instructor 3 have Prevlew Mv 32 unlimited overall recorded score I Enter attempts this-problem furction as your remaining 0%. times Submit Answers answer ] Use part / Tdu 1 4: Probiem List Thealcin Problem Next Calculus #NIRAUOD f(c) = 87 1



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Complete them to review topics relevant to the remaining exercises. Let $f(x)=\left(\frac{1}{3}\right)^{x} .$ As $x \rightarrow \infty, f(x) \rightarrow$__________.

Yeah, for this problem, in part they were asked to for the function F of X equals x squared minus one on the closed interval from zero to to use a regular partition to form to form riemann sums. Uh using the formula displayed there. So we first need to figure out what our delta X is going to be. So we can see that we have an interval from 0-2. So that means our delta X is just going to be too over N. Which in turn means that our Riemann sums can be expressed as the sum from I equals one up to uh N of now, it's F of ui so we can write this then as X I squared minus one Times two over end for part B were asked to express the limit as N approaches infinity of the Riemann sums as a definite integral. So that is going to be the integral from 0 to 2 of x squared minus one. Then for part C were asked to use a computer algebra system to find the value of the definite integral. So one moment here, I'm going to be doing that off screen as you hear my click clacking away. Well, Also I'll add that actually I need to include that DX, there but the integral is going to be to over three

And it's gonna be graphing a function. All right. So here's the function that were given affects is equal to negative three to the power of one minus X plus two. So, the first step we're gonna want to do is find the domain and range, which I've done right here. And when you plug in random numbers in the X. For the X. And substitute it. And you will find out that this function will be true for all of the X values. So it's gonna go from negative infinity to positive infinity in the range we have the liner ship right here. So we know that it's not gonna be passing to and that's gonna be your limit right there. But it will be going um below as much as it could. So that's a negative infinity to to and after that we will be finding the X intercepts. And the Y intercept. Have done right here as well. To save us some time. And this is where differentiation comes in. So we're gonna go ahead and plug in. The natural log of two. Negative natural log of two plus negative natural log of three. All over the natural log of three. And if you think about it three on the the natural log of three on the top and the natural log of three on the bottom will be canceling out and leaving us with the negative natural log of two which is actually going to give us a point yeah 369 or approximately 0.369 So it's good to write that down and the X value is gonna be shooting zero where the y value is going to be zero in this situation the y value is going to be zero and the y intercept is actually one negative one because we're gonna be starting out at negative three and then plus two will give us negative one. And after finding the domain range extender set and y intercept, we're gonna want to find the horizontal and santo vertical as santo and extreme points. There are no extreme points and there are no vertical ascent owes. But there is a horizontal santo which is Y equals two. All right. Now let's get into graphing. And what is the horizontal has come to mean? It means that the graph will not go past white too. And since we'll be going to the negative side, let me go ahead and create my margin right? Without here should probably keep going miss that. And another one right here. My ex line. All right, now let's do the actual graphing part. So I should probably mark this. So, let's give that a 12 Uh huh. Three. Yeah. In here, negative one. Mm. Mhm. That's human and NATO. One two. All right. So now let's go to the actual graphing part finally. So let's apply and plot in what we know we know that there is an A sento at Y. Equals two. So, we're gonna wanna first draw a line. We do that red to let ourselves know that we're not going to pass this. Actually let me make this a dotted line. Yes. And we will not be passing life's too. All right. That was the first step. And then we're gonna have a point at negative one to indicate our why intercepts. And we're going to also have a point at right over here. Yeah. Because that's where our X. Intercepts is at. And this point will And this line right here is gonna be um 0.5. All right. Now let's go to the graphing. So it's gonna be a curve. It looks something like this. Yeah. Mhm. Yeah. And that part will go super close to two, but it will never actually touch white too. So I'm going to leave it like that. We do not do arrows in these type of functions. And this part right here is going to keep going below and to the left indefinitely. And yeah, that is how we graft dysfunction right here. And I hope you find this video helpful.

All right, we are given parentheses. X plus one the 1/3 power plus X times 1/3 times X plus one to the negative 2/3 power. We can look at this right here. Multiply this vexed by one. And we can just rewrite this just to save ourselves this step you can write. This is X over three. From there, I'm gonna start with the right side so that we know what to do with the left. We are looking at X over three. And since this is a negative exponents, we can put this expression into the denominator to make it positive. So three times exports one the positive 2/3. And then, from there we have our X plus one to the 1/3 power. We're gonna want to make this into a common denominators so we can add the's expressions together. So first, we're going to need an X plus one for the 2/3 power in the denominator. We must put it in the numerator as well. But we also need a three so we can multiply this by three as well. From there you can add these together X plus one to the 1/3 post explosive one to the 2/3 is going to be X plus one to the 3/3 which is just to be singular exports one so three times X plus one over three times Experts Juan to the 2/3. And this is also plus an X because now that we have this common denominator here, we can just look at it as an addition problem at this X rayed here on two, our original expression. And then from there you can vote by this out. Three X plus three plus fix. We re exposed one to the 2/3 power, which is just going to be four x plus three over three X plus one to the 2/3 power. That'll be richer. Thank you.

In this question. It is asking f zero. So we replaced the T to the zero. So basically anything's probable to this. 20 is one. So 10 times a month. Any quote, too 10. Thanks for watching.


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