ðŸ’¬ ðŸ‘‹ Weâ€™re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Like

Report

No Related Subtopics

Johns Hopkins University

Campbell University

Idaho State University

Boston College

00:06

Jeffery W.

If $f(x)=x+\sqrt{2-x}$ and $g(u)=u+\sqrt{2-u},$ is it true that $f=g ?$

0:00

Kim H.

Jsdfio K.

00:59

Andy S.

Create your own quiz or take a quiz that has been automatically generated based on what you have been learning. Expose yourself to new questions and test your abilities with different levels of difficulty.

Create your own quiz

Okay, so we want to use a linear ization or, in other words, a tangent plane approximation to approximate this number. And now the first thing you should think is well, I know how to find the tangent plane of a point of a function of two variables. But where is my function of two variables? Well, this is where we actually have to do a little bit of thinking and say, Well, let's let our function be Well, this is the square root of something a little bit more than three. So we'll just say That's X squared. And then this is plus something a little bit bigger and our sorry, a little bit smaller than four. So we'll just let that be why and notice that what I want is f of 3.1 3.9. And of course, we could just throw toe throw that in a calculator. But we want to get an approximate value. So I have this quantity. What is it? Approximately. And I want to do this just using pen and paper. If I could use a calculator, there's no point in doing this. Eso We're kind of doing it old school. So here. What are we going to dio? We're going to find the linear approximation or the tangent plane at a special point. And of course I want my point to be pretty close to the 0.0.3 point one 3.9. But I hope that I can pick a point close to that point. That's easy to evaluate in my function. Well, the point that I'm gonna choose is 34 And now why is that? Because what happens if I plug in X equals three and my equals four? Well, this is nine plus 16, which is 25 square it a 25. It's five, so it's easy to evaluate. So what do we need for the tangent plane? Well, we need the partials. So the partial with respect to X is going to be X over square root of X squared plus y squared. Just a little bit of chain role F y is going to be why over square root of X squared plus y squared. And if I evaluate at the 0.34 notice that I get 3/5. If I evaluate the partial with respect, why 3/4? The three coming for I get 4/5 and notice that we're a said f of three comma four. It's five. So the tangent plane is going to be well, the change in X, which is 3/5 times X minus three plus changing why rate of change and why times why minus four and then plus the function value +34 which is five. So there's the tangent plane. And now I want to use the standard plane or the miniaturization to approximate this value. So let me just plug in 3.1 for X and 3.9 for Why? So if I plug that in, I get 3/5 times 3.1 minus three plus for fifth times 3.9 minus for plus five. But what is this? This is this'll is going to be zero point one. Yeah, so let's see. Ah, 3/5 0.6, right? Yeah, 0.6 times. So your 0.1 plus 4/5 0.8. And then times, this is gonna be minus. So your plan one and then I'm gonna add five like that. Okay, So what is this? Well, this is just going to be zero point 06 minus 0.8 plus five. Okay. And so what is that? That's going to be minus two hundreds from five. So that's going to be 4.9 eight. So this number is approximately 4.98 and I would encourage you to get out your calculator and be amazed at how accurate this linear approximation. Actually, it's

Multiple Integrals

Vector Calculus

33:18

01:38

06:52

09:20

06:47

07:55

04:57

06:55

04:59

08:13