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

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

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

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

satellite73 Group TitleBest 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
 2 years ago

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

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

iop360 Group TitleBest 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
 2 years ago

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

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
what is \(f(13)\)?
 2 years ago

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

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

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

satellite73 Group TitleBest 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
 2 years ago

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

satellite73 Group TitleBest 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
 2 years ago

iop360 Group TitleBest 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
 2 years ago

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

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

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

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

satellite73 Group TitleBest 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
 2 years ago

iop360 Group TitleBest ResponseYou've already chosen the best response.0
ohh ok thanks!
 2 years ago

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