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Find the limit: see the attachment. Please, don't throw around the word derivative, just yet.
 one year ago
 one year ago
Find the limit: see the attachment. Please, don't throw around the word derivative, just yet.
 one year ago
 one year ago

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MoonlitFateBest ResponseYou've already chosen the best response.0
I can do the first step, which I think is to rationalize the numerator, but then I get stuck.
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
rationalize the numerator by multiplying top and bottom by the conjugate of the numerator when you do, the \(\Delta x\) will cancel
 one year ago

MoonlitFateBest ResponseYou've already chosen the best response.0
Then I get: \[\frac{ 1 }{ \sqrt{x + \Delta x } + \sqrt{x}} \]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
\[\lim_{h\to 0}\frac{\sqrt{x+h}\sqrt{x}}{h}\times \frac{\sqrt{x+h}+\sqrt{x}}{\sqrt{x+h}+\sqrt{x}}\] \[=\frac{x+hx}{h(\sqrt{x+h}+\sqrt{x})}\] \[=\frac{h}{\sqrt{x+h}+\sqrt{x}}\] \[=\frac{1}{\sqrt{x+h}+\sqrt{x}}\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
lol i was writing instead of looking at what you wrote
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
now take the limit by replacing \(\Delta x\) by \(0\) and get \[\frac{1}{2\sqrt{x}}\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
which happens to be the "DERIVATIVE" (yeah, i know) of \(\sqrt{x}\) a good one to memorize
 one year ago

MoonlitFateBest ResponseYou've already chosen the best response.0
Wow. Funny how the small steps confuse me, yet, I can do most of the "hard" things...
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
true, you did all the hard work replacing \(\Delta x\) by zero is rather simple
 one year ago
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