Question

find horizontal asymptote of function y=x/sq rt (x^2+1)

i keep getting horizontal asymptote=0 but the graphing calculator has HA =1,-1
what did i do wrong

Answer 1

\[\frac{x}{\sqrt{x^2}}=\frac{x}{|x|}\] which is either 1 or -1 depending on the sign of \(x\)

Answer 2

as x approaches infinity the 1 is insignificant. then using L'Hospital's rule the derivatives are going yo be 1 or -1 with -infinity