find the limit as x approaches infinity of (4x-7)/((5x^2)+3x+7)

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find the limit as x approaches infinity of (4x-7)/((5x^2)+3x+7)

Mathematics
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\[\lim_{x \rightarrow \infty}\frac{ 4x-7 }{ 5x ^{2}+3x+7 }\]
We haven't gone over limits as x approaches infinity in class before.
divide it all by the highest power of x to simplify. anything left with an x in the denominator will zero out since 1/inf is a very very small amount of cake to get

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Other answers:

so multiply the denominator by 1/x^2?
your basically searching for any horizontal asymptotes ... you covered them yet?
top and bottom yes
there are 'rules' which you can commit to memory if you have the gigabytes to play with :)
so I'm left with \[\frac{ \frac{ 4 }{ x }-\frac{ 7 }{ x ^{2} } }{ 5+\frac{ 3 }{ x }+\frac{ 7 }{ x ^{2} } }\]
now everything with an x under it, goes to something very very small, they approach zero. what are we left with?
1/5?
powers of x that is ... 4/x - 7/x^2 is not 1
-1?
0-0 = ??
oh so the answer is 0?
yep
because 0/5=0
one rule, if the bottom is a higher degree than the top, as x approaches infinity, the limit is zero
if they are of the same degree, they limit to their leading coeffs .. its just simpler to divide off by the highest power of x and assess

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