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

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

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

iop360Best ResponseYou've already chosen the best response.0
\[\lim_{h \rightarrow 0}\frac{ \sqrt[3]{1695  8x^2} 7 }{ h } \]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
same 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
 one year ago

iop360Best ResponseYou've already chosen the best response.0
the answer is \[\frac{ 208 }{ 147 }\] i want to figure what to do to get it.
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
have fun but you can do it use \(a=\sqrt[3]{16958x^2}\) and \(b=7\)
 one year ago

iop360Best 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
 one year ago

iop360Best ResponseYou've already chosen the best response.0
if f(x) is \[\sqrt[3]{1695  8x^2}\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
what is \(f(13)\)?
 one year ago

iop360Best ResponseYou've already chosen the best response.0
\[\sqrt[3]{1695  8x^2} \] with 13 plugged in, which equals 7
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
ok then you can start with \[\frac{\sqrt[3]{16958(13+h)^2}7}{h}\]\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
you can leave it in this form, or you can write \[\sqrt[3]{343h^2208h}7\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
who gave you this problem? this really sucks unless you are supposed to use a shortcut, namely recognize this as the derivative and evaluate
 one year ago

iop360Best ResponseYou've already chosen the best response.0
university online homework
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
do 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
 one year ago

iop360Best ResponseYou've already chosen the best response.0
i do know, im not sure if it would give me the answer im supposed to get
 one year ago

iop360Best ResponseYou've already chosen the best response.0
ill try taking the derivative
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
this is the derivative of \[\sqrt[3]{16958x^2}\] evaluated at \(x=13\)
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
so if you can take the derivative, then plug in 13, you will get your answer
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
just to finish quick derivative is \[\frac{16x}{3(16958x^2)^{\frac{2}{3}}}\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
by 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
 one year ago

iop360Best ResponseYou've already chosen the best response.0
yeah i think i got the same
 one year ago
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