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MoonlitFate
 3 years ago
Find the limit: see the attachment. Please, don't throw around the word derivative, just yet.
MoonlitFate
 3 years ago
Find the limit: see the attachment. Please, don't throw around the word derivative, just yet.

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moonlitfate
 3 years ago
Best ResponseYou've already chosen the best response.0I can do the first step, which I think is to rationalize the numerator, but then I get stuck.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0rationalize the numerator by multiplying top and bottom by the conjugate of the numerator when you do, the \(\Delta x\) will cancel

moonlitfate
 3 years ago
Best ResponseYou've already chosen the best response.0Then I get: \[\frac{ 1 }{ \sqrt{x + \Delta x } + \sqrt{x}} \]

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0lol i was writing instead of looking at what you wrote

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0which happens to be the "DERIVATIVE" (yeah, i know) of \(\sqrt{x}\) a good one to memorize

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0true, you did all the hard work replacing \(\Delta x\) by zero is rather simple
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