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iop360
 2 years ago
find the limit as h approaches 0:
f(13+h)  f(13) divided by h
if f(x) = ³√1695  8x^2
iop360
 2 years ago
find the limit as h approaches 0: f(13+h)  f(13) divided by h if f(x) = ³√1695  8x^2

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Algebraic!
 2 years ago
Best ResponseYou've already chosen the best response.0\[ ³√1695  8x^2\] ?

Algebraic!
 2 years ago
Best ResponseYou've already chosen the best response.0seems unlikely... missing something?

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{h \rightarrow 0}\frac{ \sqrt[3]{1695  8x^2} 7 }{ h } \]

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1same gimmick as with a square root, rationalize the numerator, but this time instead of using \[(ab)(a+b)=a^2b^2\] you have to use \[(ab)(a^2+ab+b^2)=a^3b^3\] so it is a pain in the arse

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0the answer is \[\frac{ 208 }{ 147 }\] i want to figure what to do to get it.

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1have fun but you can do it use \(a=\sqrt[3]{16958x^2}\) and \(b=7\)

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{h \rightarrow 0} \frac{ f(13 + h)  f(13) }{ h }\] this is the original question btw

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0if f(x) is \[\sqrt[3]{1695  8x^2}\]

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0\[\sqrt[3]{1695  8x^2} \] with 13 plugged in, which equals 7

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1ok then you can start with \[\frac{\sqrt[3]{16958(13+h)^2}7}{h}\]\]

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1you can leave it in this form, or you can write \[\sqrt[3]{343h^2208h}7\]

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1who gave you this problem? this really sucks unless you are supposed to use a shortcut, namely recognize this as the derivative and evaluate

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0university online homework

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1do you know how to take a derivative? because then it it would be not so hard but if you do not, then there is a ton of work to be done

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0i do know, im not sure if it would give me the answer im supposed to get

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0ill try taking the derivative

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1this is the derivative of \[\sqrt[3]{16958x^2}\] evaluated at \(x=13\)

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1so if you can take the derivative, then plug in 13, you will get your answer

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1just to finish quick derivative is \[\frac{16x}{3(16958x^2)^{\frac{2}{3}}}\]

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1by the chain rule and power rule replace \(x\) by 13 and you should get your answer this is a much snappier way then doing it by hand

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0yeah i think i got the same
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