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    Hi, i am a little confused with this concept:

    A cylinder has dimensions r=5, h=10. FInd the approximate increase in volume when r increases by 0.2 and h decreases by 0.1.

    I can get the correct answer by using partial derivatives, but dont understand why you cant just put the new set of numbers into the formula for the volume of a cylinder and compare the answers?

    Why do they give different results, and just pluggign the numbers in is wrong?

    Thanks alot.

    The point of using partial derivatives here is that it gives you a way of actually analysing how changes in the input affect the output. This is often important in understanding how a larger system behaves.

    But for the actual example, yeah, it's easier to just plug the numbers in, and you get a more accurate result that way as well. (Just plugging in the numbers is only "wrong" in that it's not what the question asks you do to. It's a perfectly reasonable way of finding the change in practice).
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