Question
Eiua End drop Ina correct domaln next to the following functlons,1, f (=)=f ()3 f (r) =[-2,5)u(5,5]u/5,(-0, 5)U(-5, 210(-2,6)(-81 2)u/"e[5,8(780,o)
Eiua End drop Ina correct domaln next to the following functlons, 1, f (=)= f () 3 f (r) = [-2,5)u(5, 5]u/5, (-0, 5)U(-5, 210(-2,6) (-81 2)u/"e [5,8 (780,o)
Answers
$f(x, y)=75 x^{1 / 3} y^{2 / 3},$ determine (a) $f(8,1),(b) f(27,8)$
All right. Um So we have a function in three variables. Um That means there's three inputs, we get one numbers and output. Um And we just want to figure out the value at these two points. Um So we're putting in four for x. Eight for y and one frizzy. So 100. We get four to the one half. 8 to the 1 3rd And 1 to the 1 6th. Those all get multiplied four to the one half is the root of four is 28. The one third is the cube root of eight which is also two and then one to the 161. So that's a total of 400. Let's do the same thing again. This time we're putting in 16 for X. 27 for Y. for Z. So 116 to the one half Times 27 to the 1/3. I am 64 to the 1/6. Okay, the square root of 16. S. Four. Key route of 27 is three. Sixth. Route of 64 is too you may not have known that but it is certainly welcome to use a calculator for these. If you don't know them. Get 2400
So for this problem, they want you to use the results from exercise 75 to, uh, calculate the derivative eventful decks. So for this problem, half of Mexico said three x minus one Teoh third power. So using the formula for from exercise 35 it says for a function in the form of I'm ax plus B to the N with relative of that function equals two end times and times and express be, in the end, minus one power and looking at the two functions going really that chemical said three be was the negative one and and equals a three. So plugging these variables in we get nine and times on equals to nine times three eggs, minus one square. This is your derivative for the function.
We have to integrate the function. Small effects divided by Okay, fetal effects Within the limits of who went to three. Okay let I assume that this integration if it was to capitalize and I we'll figure substitution that is capital effects. That was to be. This provides me at 10 checks the exit was to duty and at the place of capital of dash X. We can write small effects. Yes it was too deep since it is given in the condition. Okay. No we also have retained the limits because the old one stands for X Better one and 3. So we're able to find her teeth. That is new wherever from here we can see that he's affects so yeah Only here for three and from the table you know the well over one it is 16 period 16 And well over today's 31. So here 13. Okay. No we make substitutions Then we can say that the new limits are 16-31 And they will be placed over the next 30 years. Here we have to put duty. I know the place of capital actually have to put the 13 Generation is not the and no we have to put their limits If people 30. But then we get 12 or 13 and after their dryness low of 16 and it will be a lady properties of law. Then my final answer is about 31 x 16. Okay. And this also can be written as 0.661 if we use it radios. Okay. So both are the year answer 0.66 when he goes on and love 31 was 16 years also answered.
There is a function we have to integrate and uh LTD neither too. You opened five and the function is to give our capital attacks fx or dx ok. No day as unique as I by such a dude here. Capital effects. It was to be then I get it's a derivative desserts. DX it was too dirty and in the human version there is a condition that have dash X is equal is too small. It packs in the extra duty. Okay. No we have to go change the limits. Also that what are the value of new limits? So the old one stands for Texts that are zero and 0.5 and the new one stands will be okay so in europe That that it was zero in the next zero and the report it opened. But so Value of zero If you can see that the group and they're going to have a history certainty so I can say that the new limits of the question are Boubou three here. Okay. And the place of this effect here, that would be the poverty and a bit less of attacks we have put. Finally it's integration is it with the power T And they would take him two and 3. Then we get really killed minus the square now if I could develop Eq and yes. But then my final answer but his wellpoint 696 Okay, This is a veloute wagon say that die in 30 years that he killed my nephews. But 40 people there will be. Then I get 12.696. Okay. Thanks.