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anonymous
 5 years ago
Evaluate the following limit:
\[sqrt{(9+11x^{2})} / (6+3x)]\
anonymous
 5 years ago
Evaluate the following limit: \[sqrt{(9+11x^{2})} / (6+3x)]\

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0as x > inf and as x> (inf)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0apply La Hopitals rule

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0differentiate top, differentiate the bottom, and try again

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0y= ( 9 + 11x^2)^1/2 dy/dx = (1/2) ( 9 + 11x^2 )^1/2 * 22x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0= 11x / ( sqrt ( 9+11x^2) )

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so we want to take the limit of\[\frac{ \frac{11x}{\sqrt{9+11x^2} } } { 3}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yea, that's what i got so far

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0applying the rule again because it is still indeterminate form "infinity/infinity"

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so the (1/3) factor , bring that out then we have 11 / [ 11x / sqrt(9+11x^2) ]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so that gives what sqrt(9+11x^2) / x I think

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{\sqrt{9+11x^2}}{x}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sstill indeterminate , but if we apply the rule once more that x on the denominator will vanish

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeh I think something possibly went wrong, because it we differentiate that then we get back to 11x/ sqrt (9+11x^2)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I would just go with dominate term analysis here I think

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I would just go with dominate term analysis here I think

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0when i apply the lospitl rule i don't have to do a quotien rule between the two func tion right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i got the answers right thou thanks to inf is sqrt11/3 and to (inf) is sqrt11/3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0dominate term up the top is \[x \sqrt{11}\] the dominate term on the bottom is x ( obviously )

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so the quotient of these gives the answers sqrt(11) , and then you remember the factor of (1/3) we had earlier

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how is it \[x sqrt {11}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do i just forget about the 9 ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{x \rightarrow \infty}\frac{\sqrt{9+11x^{2}}}{6+3x}\] \[ = \lim_{x \rightarrow \infty} \frac{x\sqrt{\frac{9}{x^2}+11}}{x(\frac{6}{x}+3)}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Becomes pretty easy from there.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Looks like \[\frac{\sqrt{11}}{3}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i didn't get how yu got sqrt11/3 from that. Did you just ignore everything that had an x ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0No. I took the limit as x goes to infinity. \(9/x^2\) will go to 0. 6/x will go to 0. The only things left will be the sqrt{11} and the 3 in the denominator.
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