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DLS
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\[\lim_{x \rightarrow \infty }\frac{x^4+2x^3+3}{2x^4-x+2}\]
DLS
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x+1 is a factor of this right?
DLS
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however,no use..
TomLikesPhysics
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I think it is one half.
Because you got up- and downstairs and x^4 which I think is a special case and in which the limit approaches the coefficents before these two identical powers of x which is 1upstairs and 2 downstairs - 1/2.
DLS
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it is 1/2 only but how
TomLikesPhysics
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If you would use the L`Hopital Rule you would end up with it.
TomLikesPhysics
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Do you want to see the calculation?
DLS
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\[\lim_{x \rightarrow \infty }\frac{3x^4+4x^3+}{4x^4+x^2+7}\]
I'm trying to do this with the same concept but i'm getting 5/7
@TomLikesPhysics ?
DLS
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+5
DLS
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*
DLS
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\[\frac{12x^3+12x^2}{16x^3+2x}\]
TomLikesPhysics
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should be 3/4
DLS
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??
TomLikesPhysics
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the one where you got 5/7
DLS
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okay got it!
DLS
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but how is it gaining infinity/infinity?
TomLikesPhysics
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How it gains infinity?
You take the limit where x goes to infinity.
So both terms grow.
Is that what you meant?
DLS
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it is something+infinity
is it samething?
DLS
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\[\lim_{x \rightarrow \infty } \frac{x^3+x^2+4}{x^2+8}\]
are you gettng 1 here?
TomLikesPhysics
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Here it should be infinity.
You got downstairs an x^2 and upstairs and x^3. So the x^3 "is stronger" and wins and therefore the whole thing goes to infinity.
DLS
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No,I solved according to what you said and got this:
\[\frac{3x^2+2x}{2x}\]
so I got 3x+1=1?
TomLikesPhysics
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How do you end up with 3x+1=1 if you got a fraction?
DLS
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\[\frac{3x^2}{2x} + \frac{2x}{2x}\]
DLS
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I ended up with:
\[\frac{3}{2}x+1\]
TomLikesPhysics
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k
but if you got 3x+1 and let x approach infinity (taking the limit) than you end up with infinity.
DLS
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okay!
if it was 1/x and x==> infinity it would have been 1 RIGHT?
TomLikesPhysics
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limit x-> inf. of ax+b is alsways infinity. The b does not matter in the long run and nether does a while x gets bigger and bigger.
DLS
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Great.Clear now :)
TomLikesPhysics
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If you got 1/x and x gets bigger and bigger you would get a limit which is 0.
DLS
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yeah!
TomLikesPhysics
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1/x as x approaches infinity is 0.
1/x as x approaches 0 is infinity.
DLS
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\[\lim_{x \rightarrow 0} \frac{\cos7x-\cos9x}{\cos3x-\cos5x}\]
These ones?
TomLikesPhysics
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I don´t know. Have not seen this one before.^^
Never dealt with limits and sine or cosine.
DLS
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okay..book did a direct step after this :|
\[\frac{2\sin8xsinx}{2\sin4xsinx} \]
TomLikesPhysics
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^^
First time I see that kind of stuff. I´m sorry but with that I can not help you.