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Ftov' give couLerexnmple Jisprat IfA 5 C then (AC C) ^(B g (b} (ABJU(BIC) =...

Question

Ftov' give couLerexnmple Jisprat IfA 5 C then (AC C) ^(B g (b} (ABJU(BIC) =

Ftov' give couLerexnmple Jisprat IfA 5 C then (AC C) ^(B g (b} (ABJU(BIC) =



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$\begin{array}{ll}{\text { (a) } A B+C} & {\text { (b) } 3 G F} \\ {\text { (c) } C K+B} & {\text { (d) } C K+H} \\ {\text { (e) } E M C} & {\text { (f) } G L H} \\ {\text { (g) } H L G} & {\text { (h) } 2 E L+5 M B}\end{array}$

Feats. Clearasil on rain here. So, for part A, we're gonna use the product rule. Let me get F G. Derivative five is equal to derivative of F five GF five less five derivative of G of five. You plug it in and you get six times negative. Three plus one times two, which is equal to negative 16. We have part being f departed by G. The derivative of five is equal to the drill bit it, uh, the five g of five minus F five. The derivative of chief of Fly all over G of five square and you get six times negative. Three minus one times two over a negative three square, giving us negative. 20 over nine For part C, you have Jeanne divided by s the derivative five, which is equal to the derivative of G of five. Yes, a five minus g of five. The derivative of F of five all over five square. This is equal to two time one minus negative. Three. I'm six over one square, which is equal to 20

Substitute all the exes and Jia vacs with after backs, so three effort backs. This is equivalent to 15 over X squared, plus Juan. Now substitute two frocks. 15 over two squared plus one equals three.

Given equal to metrics? 5 8 -7. 32 and eight transports. Mhm. Is 58 3 -72. We need to find a transposed. Then that is equal to 25 a square plus the square 15 A -2 p. then 15 A -2 p. 9-plus 4. The thing. Okay so that a transport is equal to 25 A square plus B sq 15 A minus to B. 15 A minus to B. And 13th. Okay now we know that a endure kind of A. Is equal to determinant A hindu. Since I since this is the uh two by two matrix we can write A two. Okay it's okay that is equal to a hindu gender face. That is 10 A. Plus three B. Zero zero. And A. This three B. Thank you. You can find using and a joint of it. Yeah if you need I will write okay equal to five minus B. 32 and are joined our phase in the changing these two elements and changing the sign of these elements. Okay. Of 10 8 plus three B zero. Okay this matrix itself we get these metrics. Now this this one. Okay so a transport equal to a and you are joined of A. We have so creating corresponding elements we get 15 8- to be equal to zero. It is 15 a. equal to to be Mm applies equally to buy 15 b. Okay then 10 a plus three be equal to 13 instead of a weekend right to buy 15 B Plus three be equal to 13 three. This is two, four by three B Plus three. Be equal to 13 for by three plus three. That has 13 battery. So 13 by three B is equal to 13 which implies big 12 to 13 Angel three x 13 sequel to Before we got B- 23. If be equal to three, then is equal to to buy 15 into three. That is Equal to two x 5. Okay, we need to find five A plus B. That is equal to five into a. is two x 5. Yeah. Plus these three so 55 court council and two plus three is five answers five

So we have g prime G prime of T to be cool too. So a C let's be the NJ prime prime of T. It's going to be equal to two. Mm. So the next thing to look at is replace See by one in the expressions of G g prime n G program to obtain systems of equations. So then this implies that you have so we have G of one, it's equal to five G. of one. We give us three. The N G prime prime of when will be equal to mine? It's full. So this implies that we have A plus B. Let's see equal to five. Then you have to a plus Be equal to three. Then you have to a call to negative for here, which implies DATs, see it's going to be equal to so see here is going to be going to five minus a minus B And this is going to be equal to five Plus 2 -7. Then B is going to be equal to three -2 A which is equal to three Bloods four. Then a is going to be got to -2. So then it's in place that you have See to be called zero be equal to seven and a equal to -2. So this implies that's our gtc. The function It's going to be called to -2 C squared blood serving. See? So these are the values of A. B n. C. And this is a function as well. He's fine ari.


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