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Dkplacomentparkle mutT4 (0) Frtd IFe avcragc vccoty Otar auchIEIA4 AKnemnneltMaed Heipil...

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Dkplacomentparkle mutT4 (0) Frtd IFe avcragc vccoty Otar auchIEIA4 AKnemnneltMaed Heipil

dkplacoment parkle mutT4 (0) Frtd IFe avcragc vccoty Otar auch IEIA4 A Knemnnelt Maed Heipil



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complete the following table for y = f(x) = 3x ^ 2 and the indicated value of a = 2

0.1-0.01-0.001 0 leftarrow0.001 0.01 0.1 ? ? ? ? ? ? ? f(a + h) - f(a)

The jury a central Trillo pre redina and anna. Lena. For simple structures. Language symbols, we have the describe the land stockton confirmation and Sandman atomic. A young clearly symbols concern elemental simple surrounded. That's for each for balanced electrons. For here we have the the chemical compounds of hydrogen, nitrogen, Nigerian, hydrogen. This one is about carbon, hydrogen energy and this one is very demanded only night again. This are million and it has nitrogen had again. This is the chemical symbol but very molecular. Uh huh orbit are less defined for like this one for example, we have pause. Mhm Well or been me and energetic. All the Leicester baton is not as les mis muskrats baby most perilous element is only a 10 minute calls come back. It's a bonus. And representative Allen Iverson Smp. When Energy girl enable. Np. Yeah.

In this problem we have a cellphone dioxide molecules where the cell for ma'lik sulfur atom has center at origin and we have to find out the X coordinate of the center of mass of the molecule. Yeah. Mhm. Yeah. Yeah. No for each of the oxygen atoms or sell food items. Their center of mass lies at their center. So for oxygen atom the X coordinate of center of mass is minus excellent. And similarly for dark season under that outside has X coordinate as plus X. One. And the cell for adam has in the center of mass at origin. So for self right. Um the the coordinator of center of mass will be zero. No, the centre mass of molecule is X cm. This is the X coordinate of center of mass equal to mass of oxygen times six. For one it is the center of mass off X coordinate of center of mass of oxygen plus M. S. X. S. S. M. O. X. Or two. Yeah, M O plus M S plus M O. The other some of them are sort of oxygen and several items. No mass of oxygen times. For the left we have X coordinate of minus X. One. Yeah, for right for self or we have zero. I thought right. Obscene atom behalf X coordinate as plus X. One. Yeah. Both oxygen attempts have the same magnitude of X coordinate of central mosque because they are at same distance from the Origin. And angle is also same at 60°. It can be proven Because this angle is 30° here at this angle 30°. So art will be equal to, sorry. The X coordinate of I have seen atoms will be x equal to our cost 30° And are the same for both. And 30° is also same for both. So both have same magnitude of X coordinate, so minus AM AM not X one plus, I'm not explain will cancel out and this is already zero. So total X coordinate of center of mass will be zero. This completes the solution. Thank you.

What the derivative of G equals. When we said it equal to zero, we first need to find what g of X equals when we set it to zero. Let's start by setting this equation right here in for zero. If we plug in as you enter G, we don't know what it is because we don't know what it is. Plus muggins here for X. It's gonna be time. Zero sign of G 20 is equal to zero squared. Okay, now, let's all this out to find what G of zero equals. This is just gonna This is gonna cancel out because it's multiplied by zero and this is also just equal zero cost zero scored a zero. So this means g of zero is also equal to zero. Now, to find the derivative of G for zero, we can rewrite our equation in terms of Y and X g of G of X will equal why and the derivative of G of X will equal Why prime or a derivative of wife are we read it right here. Okay, Now we can solve our new equation. Using implicit differentiation, we can start by differentiating both sides of the equation in respect facts. Okay, I'll serve the left side of the dream of Why is it just gonna be one? But since your differential and respect to X, it's going to be why Prime, you know, we have a product rule will start with a group of X, which is this one. So it's gonna be just sign why? Plus our derivative of sign of why. Which is co sign of why. But since we're differentiating in respect to act, it's going to look like my wife prime again. This is all equal to two x are derivative of X squared. Okay. And now what we can do is isolate for our Why prime variable. So what I'm gonna do is just a subtract sign. Why from both sides and also factor out why prime from these two. Okay, that's factored out. And on the other side, we're gonna have to x minus sign of why. Okay. And I want to divide both sides by one plus x coast and why to solve for y prime. Okay. And now would that we've used implicit differentiation to solve for R Drood of of why or which is equal to our derivative of G. We can rewrite this all back in our original variables. Next is the same, but it's gonna be sign G of X all over one times x co sign G of X. And now we could do is plug in for zero because we have Oliver values as G of zero is also equal to zero and plug in zero for exits. Also zero. Was that in down here? Okay, Now, if we plug this end Ah, Sign of zero is equal to 21 zero. Sorry. It's able to zero. So on the top, we're just gonna have 220 which is zero minus zero. So it's all zero all over. One plus zero temps go, son of zero. So it's over one that is also with one. And this is your answer or the derivative of G when we plug it in for zero, that is also equal to zero. And that's your answer.

So in this question we want to complete the following table for Y equals f. Of X equals three X squared. And the indicated value of a equals two. So I'm looking at this expression here and they're telling me my a. Is too swan looking at F. of two plus H -F. of two being divided by each. So what is f. of two plus age? Well my F. Of X. Is three X Square. So what f. of two plus age means is everywhere I see an ex I replace it With the quantity of two plus H. So f. of two plus H. This time is three times two Plus H Quantity Square -F. of two. Well If f. of two but there well that's three Times two Squared. I'm plugging into f of X three times 4. That's 12. So three times two plus H quantity squared minus 12 being divided by H. Now I'm going to simplify this by expanding out The two Plus H Quantity Square. When I do I get four plus four H plus H squared. This is -12. While being divided by each. If I distribute that three I've got 12. Was 12. Each plus three H squared minus 12 being divided by H My 12. They cancel out I'm left with 12 h. Plus three H squared being divided by each. In the numerator there is a common factor of H. I can cancel that or I can factor that out leaving me with H times the quantity of 12 plus three H divided by each. Common factor of H. In the numerator and denominator cancels out. I am just getting 12 Lus three H. And so I am getting for this expression here. 12 Lus three H. Okay. And now all I do is I plug in each of these H. Values. So I've got 12 plus three Times negative .1 And I get 11.7 and then I plug in negative .01. Instead If I plug in negative .01 I get 11.97. So then I get 11 point 97. If I plug in negative 0.1 I get 11 point 997. Now if you came from the right instead if you plug in .1 you get 12.3. If you plug in .01 You get 12 oh three. And if you plug in .00.1 You get 12.0 three. What are these numbers getting closer and closer to? As H approaches zero. These numbers are getting closer and closer to 12. Hopefully this is helpful and makes sense. Have a great rest of your day


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