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anonymous
 4 years ago
Finding the Derivative: Find (h^(10))(2), or the 10th derivative when x=2. h(x)=1=2(x2)+6(x2)^2+...+(n+1)!(x2)^n+...
anonymous
 4 years ago
Finding the Derivative: Find (h^(10))(2), or the 10th derivative when x=2. h(x)=1=2(x2)+6(x2)^2+...+(n+1)!(x2)^n+...

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TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0the only part we need consider is the that with\[n\ge10\]because all other terms vanish. That would be\[11!(x2)^{10}+12!(x2)^{11}+\dots+(n+1)!(x2)^n\]after the tenth derivative this will be\[11!\cdot10!(x2)^0+12!\cdot11!(x2)^1+\dots\]\[\dots+(n+1)!\cdot\frac{n!}{(n10)!}(x2)^{n10}\]all the terms after the zero exponent are junk and vanish when x=2, so we are left with\[f^{10}(2)=11!\cdot10!\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0but what about the zero exponent? if 2 is plugged into the second to last step, or11!⋅10!(x−2)^0, it will become 11!10!(0)^0. Does the 0^0 just cancel out?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0that is a very good question...

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0wolfram considers it defined http://www.wolframalpha.com/input/?i=d%5E10%2Fdx%5E10%5B%28x2%29%5E10%5D+at+x%3D2 but I have no real insight on it :/
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