clara1223
  • clara1223
find the limit as x approaches infinity of (4x-7)/((5x^2)+3x+7)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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clara1223
  • clara1223
\[\lim_{x \rightarrow \infty}\frac{ 4x-7 }{ 5x ^{2}+3x+7 }\]
clara1223
  • clara1223
We haven't gone over limits as x approaches infinity in class before.
amistre64
  • amistre64
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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clara1223
  • clara1223
so multiply the denominator by 1/x^2?
amistre64
  • amistre64
your basically searching for any horizontal asymptotes ... you covered them yet?
amistre64
  • amistre64
top and bottom yes
amistre64
  • amistre64
there are 'rules' which you can commit to memory if you have the gigabytes to play with :)
clara1223
  • clara1223
so I'm left with \[\frac{ \frac{ 4 }{ x }-\frac{ 7 }{ x ^{2} } }{ 5+\frac{ 3 }{ x }+\frac{ 7 }{ x ^{2} } }\]
amistre64
  • amistre64
now everything with an x under it, goes to something very very small, they approach zero. what are we left with?
clara1223
  • clara1223
1/5?
amistre64
  • amistre64
powers of x that is ... 4/x - 7/x^2 is not 1
clara1223
  • clara1223
-1?
amistre64
  • amistre64
0-0 = ??
clara1223
  • clara1223
oh so the answer is 0?
amistre64
  • amistre64
yep
clara1223
  • clara1223
because 0/5=0
amistre64
  • amistre64
one rule, if the bottom is a higher degree than the top, as x approaches infinity, the limit is zero
amistre64
  • amistre64
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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