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DRico
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would lim(x approches infinity) (sqrt(x^2+1))/(2x+1) be DNE since it would basically be infinity/infinity?
 2 years ago
 2 years ago
DRico Group Title
would lim(x approches infinity) (sqrt(x^2+1))/(2x+1) be DNE since it would basically be infinity/infinity?
 2 years ago
 2 years ago

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klimenkov Group TitleBest ResponseYou've already chosen the best response.3
What is DNE?
 2 years ago

DRico Group TitleBest ResponseYou've already chosen the best response.0
does not exist
 2 years ago

redham Group TitleBest ResponseYou've already chosen the best response.0
That is indeterminate form, so you can't say it doesn't exist. You will have to manipulate it to use L'hopital's
 2 years ago

klimenkov Group TitleBest ResponseYou've already chosen the best response.3
\[\lim_{x\rightarrow\infty}\frac{\sqrt{x^2+1}}{2x+1}=\lim_{x\rightarrow\infty}\frac{\sqrt{\frac {x^2}{x^2}+\frac1{x^2}}}{\frac{2x}x+\frac1x}=\lim_{x\rightarrow\infty}\frac{\sqrt{1}}{2}=\frac12\]
 2 years ago

klimenkov Group TitleBest ResponseYou've already chosen the best response.3
@redham L'hopital's is not the best idea.
 2 years ago

Valpey Group TitleBest ResponseYou've already chosen the best response.0
No, you can map a limit here.\[\lim_{x \rightarrow \infty}\Big(\frac{\sqrt{x^2+1}}{2x+1}\Big)=\frac{\lim_{x \rightarrow \infty}\Big(\frac{d\sqrt{x^2+1}}{dx}\Big)}{\lim_{x \rightarrow \infty}\Big(\frac{d(2x+1)}{dx}\Big)}\]
 2 years ago

DRico Group TitleBest ResponseYou've already chosen the best response.0
how do i simplify to sqrt(1)/2
 2 years ago

klimenkov Group TitleBest ResponseYou've already chosen the best response.3
\[\lim_{x\rightarrow\infty}\frac{\sqrt{\frac {x^2}{x^2}+\frac1{x^2}}}{\frac{2x}x+\frac1x}=\lim_{x\rightarrow\infty}\frac{\sqrt{1+1/x^2}}{2+1/x}\] \(1/x^2\) and \(1/x\) are almost 0 when x goes to infinity. so only 1in numerator and 2 in denominator are left.
 2 years ago

redham Group TitleBest ResponseYou've already chosen the best response.0
@klimenkov I was actually thinking of squaring the denominator under the radical and then using L'Hopital's. Not from the start
 2 years ago

DRico Group TitleBest ResponseYou've already chosen the best response.0
thnaks to all of you
 2 years ago

DRico Group TitleBest ResponseYou've already chosen the best response.0
one more if y'all are still here how to calculate the derivative of f(x)=sinx
 2 years ago

DRico Group TitleBest ResponseYou've already chosen the best response.0
i know the derivative of sinx is cosx but i dont know how to prove it with the derivative funtion
 2 years ago

klimenkov Group TitleBest ResponseYou've already chosen the best response.3
\[\lim_{\Delta x\rightarrow0}\frac{\sin(x+\Delta x)\sin x}{\Delta x}=\lim_{\Delta x\rightarrow0}\frac{\sin x \cos\Delta x+\cos x\sin \Delta x\sin x}{\Delta x}=\]\[\lim_{\Delta x\rightarrow0}\frac{\sin x (\cos\Delta x1)}{\Delta x}+\lim_{\Delta x\rightarrow0}\frac{\cos x\sin \Delta x}{\Delta x}=\cos x\] Try to get it. Why is it so? Why does the first limit equals to 0 and why does the second equals to cos x?
 2 years ago

DRico Group TitleBest ResponseYou've already chosen the best response.0
im not exactly sure...
 2 years ago

Valpey Group TitleBest ResponseYou've already chosen the best response.0
http://www.zweigmedia.com/RealWorld/trig/triglim.html
 2 years ago
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