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anonymous
 one year ago
find the limit as x approaches infinity of (4x7)/((5x^2)+3x+7)
anonymous
 one year ago
find the limit as x approaches infinity of (4x7)/((5x^2)+3x+7)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\lim_{x \rightarrow \infty}\frac{ 4x7 }{ 5x ^{2}+3x+7 }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0We haven't gone over limits as x approaches infinity in class before.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1divide 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so multiply the denominator by 1/x^2?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1your basically searching for any horizontal asymptotes ... you covered them yet?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1there are 'rules' which you can commit to memory if you have the gigabytes to play with :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so I'm left with \[\frac{ \frac{ 4 }{ x }\frac{ 7 }{ x ^{2} } }{ 5+\frac{ 3 }{ x }+\frac{ 7 }{ x ^{2} } }\]

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1now everything with an x under it, goes to something very very small, they approach zero. what are we left with?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1powers of x that is ... 4/x  7/x^2 is not 1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh so the answer is 0?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1one rule, if the bottom is a higher degree than the top, as x approaches infinity, the limit is zero

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1if 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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