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1a. M~N,-N F-M(5 points)1b. Q-(-P_ Qis a theorem_...

Question

1a. M~N,-N F-M(5 points)1b. Q-(-P_ Qis a theorem_

1a. M~N,-N F-M (5 points) 1b. Q-(-P_ Qis a theorem_



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(a) Prove Theorem 4, part 3.
(b) Prove Theorem 4, part 5.

And four. So it states that so part three states that if efforts continue is a day and C is constant and sees a instinct Yes. Then see, it is also continue with Well, she okay? Sure. Since I first continuous and eight, we have limit X trying toe I for fix the way to a frumpy adults that's using the constant multiple off limits we have limit extending to eat. See if we'll fix, seek winter extend to it saying to little fix that is a printer. It takes me out. Let me explain into it. You're both states. What is it going to see into the new office countries? So this candidness You're for fair seeing to you, Sophie. Water can can witness CS. Okay. Yeah. This in place C s office continuous at the end. By the definition off continue T now for section B. We have to prove bad. Five wolf serums. Let's say it's that if happened, g our continuous count active then if by G is also continuous. Okay, that GOP a is not equal to zero. So now since f n g or continue is a day we have I don't like to extend me doing it. Have profits we can do for free and limit extending to a geo fits The breaking geo that your faith is not equal to is evil. So using the caution of law off limits, John, it I mean the path well, extending to a a very G effects. You see 32 unit, it's turning to rate. It's for fakes they wanted by Geo fix. That can be, you know, nice. You mean it? Yours? Okay. Limit extend you to rate and full of rates. Invited by limit extending to eat. Do you fix? Since we know that F n g or continuous, you can write result with still see my geo fee. That was it. Quinto if by gee off Okay, which implies f B i g. This continuous repeat

Mhm. So we'll draw our picture of our little parallelogram here. We're supposed to start out with a parallelogram and that parallelogram was marked e f g h. And, um, we're going to draw this one diagonal, and we're going to label these angles now. They haven't labeled one, 234 They wouldn't necessarily have to be labeled that way, But we know our statements and reasons. We know that we're given Yeah, that e f g h is a parallel program. Mhm, which means e f is parallel to G H and ah e h is parallel thio Uh, f g. And that's my definition of a parallelogram definition of parallelogram. Mhm. Now, because of this statement, that e f is parallel to G. H. We know that alternate into your angles and we're gonna Markham Yeah, in three angle three must be congruent toe angle four because of these two being parallel. And we know that because these two are being parallel, we know that angle to an angle. One must be congruent and angle. One mhm must be congruent angle to. And that's because off go back to black, um, parallel lines, alternate interior angles. Um are we have gift parallel parallel lines altered inhales are congruent Now. We also know that we want to prove that these opposite sides are concurrent. But we have that e g segment e g is congruent to segment G E Because of the reflexive property, it's and growing congruent to itself. Therefore, we have angle side angle. We have that triangle and we'll start with E and H G is congruent and remember we have to go with corresponding part. So too is corresponding to one, so we need g f e mhm on. That's because of the angle side angle. Postural it. Now we can conclude that e h. Because it's a corresponding part segment e h must be congruent to G f Yeah, yeah. Also, we know that e f must be congruent and again labeled the right way. I'll speak and growing to G H because of corresponding parts of congruent triangles are congruent mhm and we've proven what we wanted to find

We know that the arm 5-4 is the converse of 5-1 We know that theorem five dash sex is the converse of five Dutch too. And then, lastly, we know that there are 5-7 is the converse of 5-3

You're asked Formula One here by on this just the ERM says that work getting to vector functions u and V, which are differential then read It is expected team. This song of these functions is some of the derivatives. So we're getting necker function your team you won t to when we're getting it wrong. You and the are sensible. You're in luck inside have been Do you u t plus DT is it exists very well respected t uh that you're que you won t plus the one t you too, but be to you three t What be great to you. We know that since you and here differential, I always like definition that you get the components of your year get torrential. And so it follows that each of the components of this vector our differential and so begin like that mission we have that the derivative of this vector function here exists and he didn't buy it here find with riveted of the component functions of the original functions, you won t have to be willing to and by way properties derivatives of real value you have This is you want crime t waas the one crying t you to crime T. What? Be crying. You three crying T b three Fine, Dr. Addition. It's the same. You want 20? You're three, Brianti. Well, the one trying to the to 20. The three. We recognize that a definition of derivatives of vector functions The inspector is derivative. Oh, with indication you crying Plus being connected. This is what I want to show.


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