
MHB Master
#1
September 9th, 2019,
20:21
Ok this is what I posted on MeWe in MathQuiz
I'm pretty sure this can be solved just by a quick look at the powers
But probably I could of explained it better
I know the book says to take the Limit....

September 9th, 2019 20:21
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#2
September 10th, 2019,
06:52
Yes, a horizontal asymptote involves the behavior of a function as x goes to plus or minus infinity so a limit is necessarily involved.
A "quick look" shows that A and B don't have asymptotes and that C has y= 0 as asymptote. Dividing both numerator and denominator of D by x gives $ \displaystyle \frac{5}{\frac{1}{x} 1}$ and taking the limit as x goes to plus or minusinfinity, y goes to 5. Dividing both numerator and denominator of E by $ \displaystyle x^2$ gives $ \displaystyle \frac{20 \frac{1}{x}}{\frac{1}{x^2}+ 4}$ and taking the limit as x goes to plus or minus infinity, y goes to 5.