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Invers& A= PDp-iX = (In...

Question

Invers& A= PDp-iX = (In

Invers& A= PDp-i X = ( In



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$$ \tan \cos ^{-1} x=\sin \cot ^{-1} \frac{1}{2} $$

First, divide each side of the equation by six A squared. Now find the volume. Be over two square. Be over too. Is 11 over six A 11 over six. A divide by two squared simplifies to 1 21 over 1 44 a squared. Now, at this value to both sides of the equation. And we have X squared minus 11 acts over six A plus 1 21 over 1 44 A squared equals five. Aye, sir. Three A squared plus 1 21 over 1 44 Hey, square, we can factor in us to be X minus 11 over two. A squared equals 361 over 1 44 A squared. Now that we've got this, we could take the squirt of both sides giving us axe minus 11 over to a is plus or minus. The skirt of 361 19. Squirt of 1 44 is 12 scored of a sport is a Now we have two solutions. X equals five over two A and negative to over three. A

We want to find the differential of why the y and even wait that differential for giving value effects and the ex here. The function why is equal to X squared times, natural rhythm of eggs and the value of X is want and the ecstasy going to syrup on your block So we know that differential of why is equal to the derivative of F times, the ex and that secret too. Here we have a product of two functions. So derivative is derivative of X Square is two x times the second function that's really rhythm of X plus. The first function X squared times The river tive off the second function derivative of natural over them effects is one divided by eggs. I know that times differential of eggs that is equal to two times X natural liberty them effects plus x times, the eggs. So that's the differential by in general and for the particular values given for eggs and the eggs we have that did. Differential of why is equal to two times one times natural rhythm off one plus one times the X, which is equal to 0.1 thes brother here is zero. So we have 11 times, Cyril boy 01 which is 0.1 So the differential off. Why is syrup on, sir? Want four X equal one on differential of X. You will see your bones here. One for a function y equals X squared times natural over them effects.

So in this problem, we're going to find the true change in F f of a plus de X minus half of a toe estimated change in the approximation error. So let's start out by finding the true change and the true change is going to be half of a plus d x. So that's one 0.1 Linus left of one. And if we plug all this end and get one 0.1 2/4 minus just one which equals approximately this is 1.406 Aah! Continue, Miss, Once we get 0.40604 Now for the estimated change we calculated with ah derivative of X t X. So this is the derivative of extra forthis for X Cube. So D X says a differential. Then we plug everything in. If we plug in our equals one we get four Time's our DX, which is your 0.1 So this equals 0.4 now to find the ah Ayla, we're going to subtract it from each other. And if we subtract them, we get 6.401 times 10 to the negative forth so we can say our error is less than tend to the native three

Mhm. Okay. For the given problem we want to be looking at the function G. Of X. Okay. Which equals one of her ex. And then we're gonna be looking at this one. X equals two. So we want to consider what the derivative is going to be. Well, we know that it's going to be one over X plus H -1 over X. We want to get the common denominator. This whole thing is gonna be over H. And we're sending the limit as H go to zero. So we're going to multiply this on the top and on the bottom. And then we also know that this needs to be multiplied by X on the top and the bottom we get X minus X. Finance H. So we're going to get a negative age like this. And that means the H. Is canceled. So that becomes the one which goes away. We send H 20 and we get 10 Negative one over X squared. And that's going to end up giving us a negative 1/4 because X equals two.


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