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Hi,
I have this little problem. It has been bugging me a while. I still at high school so its nothing advanced. I tried l'Hopital rule, log, differentiation, etc. and nothing of it worked. Here it is:
Limit[(2^{x + 3} + 4)/(2^{x - 1} + 1), x -> Infinity]
The problem is that it has this wierd exponent. Anyone has any ideas?
Cheers,
Dan
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As x approaches ∞, the power of 2 terms get very large, and so the constant terms can be neglected. After that it's just using power laws and working out 2^4.
For future reference, L'Hopital is used when you need to find the limit of a fraction that would be 0/0 if evaluated (usually as x -> 0). If the fraction is ∞/∞ then you have to use other tricks.
Why did the vector cross the road?
It wanted to be normal.
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So there is no single algorithm for simplifying limits, but a whole bunch of different methods? Are there any limits that exist but cannot be solved?
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Thanks mathsyperson ...just btw what are power laws? Maybe I know but perhaps the translation differs in my language from english so I dont know what it should be exactly.
Can I do it also this way(?):
according to the rule that [x^a * x^r = x^{a+r}] so that our example will be like [2^x * 2^3]/[2^x * 2^-1] and that this way the [2^x] will cancel each other out and we will get [2^3]/[2^-1] which equals eventually [16] ...
Last edited by nox_populi (2007-06-02 12:57:56)
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Standard proof:
When f(x)->a and g(x)->b and b≠0
lim[f(x)/g(x)]=a/b
Last edited by George,Y (2007-06-02 14:11:41)
X'(y-Xβ)=0
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Ah, true enough. You're technically meant to neglect things because they're infinitessimal, rather than because they're constant and infinite terms are present.
And the power laws I was talking about are pretty much exactly what you just did in your post.
Why did the vector cross the road?
It wanted to be normal.
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I see, the power law is something like a shortcut.
X'(y-Xβ)=0
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