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Dido525
 2 years ago
Find the values of a and b so that the following is true.
Dido525
 2 years ago
Find the values of a and b so that the following is true.

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Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0I am thinking about L'Hospital's rule but I am not sure how I would apply it...

Rezz5
 2 years ago
Best ResponseYou've already chosen the best response.0well, you can separate them, then solve them

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0Yeah.... But I have two variables then.

Rezz5
 2 years ago
Best ResponseYou've already chosen the best response.0are you sure it tends to infinity?

Rezz5
 2 years ago
Best ResponseYou've already chosen the best response.0if you differentiate the variable you get nothing from a, but b will still be present, you can get b right?

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{x \rightarrow 0} (\frac{ \sin(2x) }{ x^3 }+a+\frac{ b }{ x^2 })=0\]

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0Yeah. I think you are right.

Rezz5
 2 years ago
Best ResponseYou've already chosen the best response.0ahhh, so it tends to zero?

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0Yep :P . I typed wrong.

Rezz5
 2 years ago
Best ResponseYou've already chosen the best response.0no problem, you can separate them then do the limits, you can spot it by inspection, very easily

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0I can't solve the limit of: \[\lim_{x \rightarrow 0}\frac{ \sin(2x) }{ x^3 }\]

Rezz5
 2 years ago
Best ResponseYou've already chosen the best response.0you can!! differentiate 3 times until the denominator is 1,

Rezz5
 2 years ago
Best ResponseYou've already chosen the best response.0not 1, differentiate until the denominator is a constant

Rezz5
 2 years ago
Best ResponseYou've already chosen the best response.0sin(2x)/x^3 as x tends to infinity?

Rezz5
 2 years ago
Best ResponseYou've already chosen the best response.0lol!!! im losing it today...

Rezz5
 2 years ago
Best ResponseYou've already chosen the best response.0but still, i would have thought it was zero

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0The Limit is infinity..... :( .

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0We can't solve anything then.

Rezz5
 2 years ago
Best ResponseYou've already chosen the best response.0we could, i mean if one of the variables was infinity

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0But We can't do anything with infinity.... It's not a number.

Rezz5
 2 years ago
Best ResponseYou've already chosen the best response.0wait are you sure it should tend to 0?

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0Well I would assume it should tend to a finite value.

Rezz5
 2 years ago
Best ResponseYou've already chosen the best response.0i suspect the limit should tend to infinity then for it so satisfy the limit

Rezz5
 2 years ago
Best ResponseYou've already chosen the best response.0not necessarily, it can be infinity, let assume it was infinity, then we can do the question with ease. have you done analysis by any chance?

Rezz5
 2 years ago
Best ResponseYou've already chosen the best response.0okay, no problem, assume it is infinity because i think you were right the first time round, if it was infinity just plug in infinity to the differential you had computed

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0If we did that then a would be infinity and b would not exist.

Rezz5
 2 years ago
Best ResponseYou've already chosen the best response.0b would, it would be x^2,

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0but since b^2 tends to infinity the whole thing would be 0.

Rezz5
 2 years ago
Best ResponseYou've already chosen the best response.0which would be 0, at when b/x^2 as x >0

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0Exactly. We can't work with that.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0But it's not. B/x^2 is zero, not b.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0We don't know what b is.

Rezz5
 2 years ago
Best ResponseYou've already chosen the best response.0a could be infinity, then this would satisfy the limit

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0But infinity infinity is not 0.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0No it's not. Infinity is not a number. It's a concept.

Rezz5
 2 years ago
Best ResponseYou've already chosen the best response.0that is true, i moment, i am trying to multi task, i jst remembered the proof that it isnt,

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0http://en.wikibooks.org/wiki/Calculus/Infinite_Limits/Infinity_is_not_a_number

Rezz5
 2 years ago
Best ResponseYou've already chosen the best response.0okay, you need to apply l'hpitals rule over and over again, i would recon, but first you need to put all the equation under one common factor so \[=\frac{\sin(2x) + ax^{3} + bx}{x^{3}}\]

Rezz5
 2 years ago
Best ResponseYou've already chosen the best response.0http://answers.yahoo.com/question/index?qid=20110406112720AARpKn1 here is a better and easier way of doing it the sint is taylor expansion i think, the rest is pretty self explanatory
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