anonymous
  • anonymous
find the limit as h approaches 0: f(13+h) - f(13) divided by h if f(x) = ³√1695 - 8x^2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
\[ ³√1695 - 8x^2\] ?
anonymous
  • anonymous
seems unlikely... missing something?
anonymous
  • anonymous
\[\lim_{h \rightarrow 0}\frac{ \sqrt[3]{1695 - 8x^2} -7 }{ h } \]

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More answers

anonymous
  • anonymous
k
anonymous
  • anonymous
same gimmick as with a square root, rationalize the numerator, but this time instead of using \[(a-b)(a+b)=a^2-b^2\] you have to use \[(a-b)(a^2+ab+b^2)=a^3-b^3\] so it is a pain in the arse
anonymous
  • anonymous
the answer is \[\frac{ -208 }{ 147 }\] i want to figure what to do to get it.
anonymous
  • anonymous
o i see
anonymous
  • anonymous
have fun but you can do it use \(a=\sqrt[3]{1695-8x^2}\) and \(b=7\)
anonymous
  • anonymous
thanks
anonymous
  • anonymous
\[\lim_{h \rightarrow 0} \frac{ f(13 + h) - f(13) }{ h }\] this is the original question btw
anonymous
  • anonymous
if f(x) is \[\sqrt[3]{1695 - 8x^2}\]
anonymous
  • anonymous
what is \(f(13)\)?
anonymous
  • anonymous
\[\sqrt[3]{1695 - 8x^2} \] with 13 plugged in, which equals 7
anonymous
  • anonymous
ok then you can start with \[\frac{\sqrt[3]{1695-8(13+h)^2}-7}{h}\]\]
anonymous
  • anonymous
yep
anonymous
  • anonymous
you can leave it in this form, or you can write \[\sqrt[3]{343-h^2-208h}-7\]
anonymous
  • anonymous
who gave you this problem? this really sucks unless you are supposed to use a shortcut, namely recognize this as the derivative and evaluate
anonymous
  • anonymous
university online homework
anonymous
  • anonymous
mathXL
anonymous
  • anonymous
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
anonymous
  • anonymous
i do know, im not sure if it would give me the answer im supposed to get
anonymous
  • anonymous
ill try taking the derivative
anonymous
  • anonymous
this is the derivative of \[\sqrt[3]{1695-8x^2}\] evaluated at \(x=13\)
anonymous
  • anonymous
so if you can take the derivative, then plug in 13, you will get your answer
anonymous
  • anonymous
just to finish quick derivative is \[\frac{-16x}{3(1695-8x^2)^{\frac{2}{3}}}\]
anonymous
  • anonymous
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
anonymous
  • anonymous
ohh ok thanks!
anonymous
  • anonymous
yeah i think i got the same
anonymous
  • anonymous
yw

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