Question 91245
Find the horizontal asymptote of F(x) =5x^2+1/ x^2+2x+1

horizontal asymptote is the F(x) value when x is very large.

in {{{(5x^2+1)/( x^2+2x+1)}}}

when x becomes very large constant terms and x terms are relatively small compared to {{{x^2}}} terms, so F(x) value is determined by {{{x^2}}} terms, that is

{{{(5x^2)/(x^2)}}}

which gives us 5.

So the answer to your question is horizontal asymptote is y = 5

see graph below

{{{graph(400,200,-30,30,-2,7, (5x^2+1)/( x^2+2x+1))}}}

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