Zenmo
  • Zenmo
Calculus, finding horizontal asymptote (Help me understand this solution, picture included).
Mathematics
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SOLVED
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chestercat
  • chestercat
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Zenmo
  • Zenmo
how is the HA = 0?
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Zenmo
  • Zenmo
\[f(x)=\sqrt{x^2+2}-x\] is the original equation
zepdrix
  • zepdrix
Did you understand the first step? Multiplying by conjugate.

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DanJS
  • DanJS
the bottom blows up to huge numbers, a constant over a huge number is very close to zero, and getting closer as you let the bottom grow llarger
Zenmo
  • Zenmo
is it 2|dw:1447550796679:dw| is that why the HA is 0?
zepdrix
  • zepdrix
It's because the bottom is growing much faster than the top. Take for example this limit:\[\large\rm \lim_{x\to\infty}\frac{1}{x}\]Choose a really really large x to get an idea of what's happening,\[\large\rm \lim_{x\to\infty}\frac{1}{x}\quad\approx\frac{1}{99999999999}\approx 0\]
zepdrix
  • zepdrix
Same with your problem, we have a 2 on top, stays still, while the bottom is the sum of things, so it's exploding big big big. So overall, 2/(4bajillion) = 0
zepdrix
  • zepdrix
Horizontal Asymptotes tell us what's happening way way off to the left and right of a function. So that's `why` we're taking the limit, we want to know what's happening way off to the right, when x is huge.
Zenmo
  • Zenmo
Ok, I got it now. Thanks! :)
DanJS
  • DanJS
infinity + infinity ---- (1/0) + (1/0) = 2/0 that is a determinant form --> ( c /0 ) = infinity otherwise Indterminant form would be 0/0
DanJS
  • DanJS
just saying cuz of the derivatives,

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