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anonymous
 one year ago
lim t>0 [1/(t√(1+t))(1/t)]
anonymous
 one year ago
lim t>0 [1/(t√(1+t))(1/t)]

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\lim_{x \rightarrow 16} (\frac{ 1 }{ t \sqrt{1+t} }  \frac{ 1 }{ t })\]

dinamix
 one year ago
Best ResponseYou've already chosen the best response.0(1(17)^1/2 /(17)^1/2) 1/16

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0hint: your function, is continue at t=16

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0*as t approaches 0... sorry

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0you have to replace t with 16 only

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes, the answer is 1/2 @vvvbb

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes... so how do I get there?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1440949656458:dw choose common denominator and simplify

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then you get\[\frac{ 1\sqrt{1+t} }{ t \sqrt{1+t}}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1440949891651:dw

idku
 one year ago
Best ResponseYou've already chosen the best response.1\[\lim_{t \rightarrow 0}\left[\frac{1}{ t \sqrt{1+t}}\frac{1}{t} \right]\] this?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then multiply by conjugate \[\frac{ 1\sqrt{1+t}}{ t \sqrt{1+t}} \times \frac{ 1+\sqrt{1+t} }{ 1+\sqrt{1+t} }\]

idku
 one year ago
Best ResponseYou've already chosen the best response.1\[\lim_{t \rightarrow 0}\left[\frac{1}{ t \sqrt{1+t}}\frac{1}{t} \right]\] \[\lim_{t \rightarrow 0}\left[\frac{1}{ t \sqrt{1+t}}\frac{\sqrt{1+t}}{t \sqrt{1+t}} \right]\] \[\lim_{t \rightarrow 0}\left[\frac{1\sqrt{1+t}}{ t \sqrt{1+t}} \right]\] I multiplying top and bottom times 1+sqrt(1+t) \[\lim_{t \rightarrow 0}\left[\frac{11+t}{ t \sqrt{1+t}+t(1+t)} \right]\] \[\lim_{t \rightarrow 0}\left[\frac{t}{ t (\sqrt{1+t}+(1+t))} \right]\] \[\lim_{t \rightarrow 0}\left[\frac{1}{ \sqrt{1+t}+(1+t)} \right]\]

idku
 one year ago
Best ResponseYou've already chosen the best response.1now plug in t=0 into the limit

idku
 one year ago
Best ResponseYou've already chosen the best response.1AsAAD did this before me, just now noticed:) In any case, this is a full recap then

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0OK! thank you @idku and @ASAAD123 ! Sucks that I can't give 2 best response...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@idku ^^ no problem.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0correction you missed minus sign \[\lim_{t \rightarrow 0}\frac{ 1\sqrt{1+t} }{ t \sqrt{1+t} }\times \frac{ 1+\sqrt{1+t} }{ 1+\sqrt{1+t} }\] \[=\lim_{t \rightarrow 0}\frac{ 1\left( 1+t \right) }{ t \sqrt{1+t}\left( 1+\sqrt{1+t} \right) }\] \[=\lim_{t \rightarrow 0}\frac{ 1 }{ \sqrt{1+t}\left( 1+\sqrt{1+t} \right) }=\frac{ 1 }{ 2 }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yea, i noticed it, but thank you!
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