anonymous
  • anonymous
Please help me with this problem. Also, don't use l'hopital's rule.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Find \[\lim_{\Delta \rightarrow 0}\frac{ f(x+\Delta x)-f(x) }{ \Delta x }\] When \[f(x)=\sqrt{x}\]
anonymous
  • anonymous
lets get rid of that stupid \(\Delta\) because it is too hard to write, and replace it by the usual \(h\) and write \[\frac{\sqrt{x+h}-\sqrt{x}}{h}\]
anonymous
  • anonymous
the steps are rationalize the numerator, cancel, replace \(h\) by \(0\)

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anonymous
  • anonymous
try it, if you get stuck let me know a hint is to leave the denominator in factored form, don't multiply out
anonymous
  • anonymous
So it's\[\frac{ \sqrt{x} }{ 2x }\]
anonymous
  • anonymous
I had this answer, but I wasn't really sure if it's a valid one.
anonymous
  • anonymous
oooh i see what you wrote
anonymous
  • anonymous
yeah i guess you are right, but really you want to leave it as \[\frac{1}{2\sqrt{x}}\]
anonymous
  • anonymous
Alright then. Well thank you for taking your time in helping me with this problem, Satellite.
anonymous
  • anonymous
yw

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