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QyeatlonParnLEsoap bubble Is In the shape . sphere of radius (hence surface 4m2 Using differentials, approxlmate tne Increase the soap bubble's surface Jrea wt...

Question

QyeatlonParnLEsoap bubble Is In the shape . sphere of radius (hence surface 4m2 Using differentials, approxlmate tne Increase the soap bubble's surface Jrea wthen the radlus Increases (rom To solve this question we start with cm; and the change risdr = NowdsWe Bet dS = dcelmol elaces}50 Ihe approximate increase the soap bubble'$ surface areasquare cm (ce tivc

Qyeatlon ParnLE soap bubble Is In the shape . sphere of radius (hence surface 4m2 Using differentials, approxlmate tne Increase the soap bubble's surface Jrea wthen the radlus Increases (rom To solve this question we start with cm; and the change risdr = Nowds We Bet dS = dcelmol elaces} 50 Ihe approximate increase the soap bubble'$ surface area square cm (ce tivc



Answers

A right circular cylinder has a radius of $50 \mathrm{cm}$ and a height of $100 \mathrm{cm} .$ Use differentials to estimate the change in volume of the cylinder if its height and radius are both increased by $1 \mathrm{cm}$

In the question particle moves along the curve. six y equals two x cubed plus two. We have to find the points on the kovac which the Y coordinate is changing it times as fast as the X coordinate. Now moving towards the solution here. The question of the car with six vehicles to X cubed plus two. Now considered X com away be required point on the curve one. Now, as for the given statement Divided by D Excess eight. Now From the question one six. Yeah. Six Day Bye. Bye. will be equal to three X. Square. So now moving further 16 to 8 will be called to three X square. So from here your ex well you will be plus minus four. That is to values of X are possible. Now when access four than your six Y will be Equal to 64 Plus two that his wife will be 11. So the required points are 4:10. And now when excess minus four then six Y will be called minus 64 plus two. So by will be equal to minus 31 by three. That is the required points are minus four, Common minus 31 by three. Thank you.

In this problem, we want to write to differential formula that estimates change in volume off a fear when it's radios, changes from 10 70 mirrors to 10 point Sierra, five centimeters. For that, we're going to recall the function of the volume of the fear that is 4/3 times by times radius to the third. And here are his radius of this fear and V E. C. Volume of this year. So, uh, we can say that the differential off the volume sequel to Did derivative respect to our of 4/3 off by times are to the third differential of our That's equal to 4/3 bye times three are square differential off our and that's equal to simply find these terms. Yeah, it is equal to four times. Bye. Our square differential are so the formula to calculate or estimated change in volume when there is a change in the radius of a sphere, ease differential of volume equals for pie. Our square differential of radius It is a formula, and now, as we know that the radio's changes from 10 to 10 point C five centimeters, we know that the differential of radios a change in the radius is syrup 0.5 So differential or changing volume is going to be four times by radios, which is stand centimeters square times differential of radios, which is the variation of the radios, which is syrup 0.5 centimeters. And that C one too. 20 bye centimeters to this, sir. Then we can say that the variation of the ah variation mean volume of this fear. When the radius changes from 10 centimetres too temple, 10.5 centimeters. It's approximately 25 20 times by centimeter square.

Okay, so the lateral surface area of a cone Circular cone It is pi our square it of our squared plus h squared. And we want to approximate the total change in s when r changes by D. R and age doesn't change fixed. Okay, so don't s is going to be approximated by this linear approximation. A differential of s. And what is this? What's the derivative with respect to our times, the change in honor. So we have high square it of r squared. Hey, squared Wes, Hi are over too square it of r squared H squared times to r And then all of this times deeper you. So here's just the during its vast with respect to our and then the total change in s is just given by its approximated by the derivative. At that point, our times to change

Surface area as ICO job by our times with a square root under our square bus at square on the question asked me to find the ask the different show formula. Uh, when the uh goes from my arse approaching the answer blessed the are So this means that in this question, hander arm will be the variable aan den. The arch here will be a constant there followed the s by formula every go to, uh, s Bram under our times br And here l a to find the s Bram that said you did a letter to do it on the side here. So as Bram, uh, and we go Jew here way Notice that we have to function here and we need you Lied about it rule here you Tempe's really really Terry coaching you from three just you three, Bram. And if our esperan are Waco Teoh by and the rift in the article two pi times square it on the r squared plus at square. And now Plus now that the review the with attempts by our times that the review of the square root on the X Square plus at square and where it goes to one divided by a squared off this square. So it's again that are scoreless. Our square bliss out square Thames was the, uh, square Bliss Square, Bram, and isn't should be minus near on. We can continue more stamp. And then we see here that I really love this one because our trains a constant So we get it. Could you zero And they lived in the r squared to our with this are so together miners to get minus Bryant on square dividing by asked us out square So as a way again, that s our Bram We should be able to find any ass. Now they're found that the asked it will echo to buy square it on the Esquire plus at square minus by our square off a Scrabulous square on now doesn't br zero now we but also not the are so this will be the answer for that. They asked


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