y= 1+(1/x)(sin(x^2)) find this asypmtotes please

Question

anonymous · Answer

Welcome to OpenStudy 

no asymptotes. one might think "x=0" might lead to an symptote but if you take a limit at x=0+ and x=0-, you find that y=1.

tkhunny · Answer

Define "asymptote".  How about $y = 1+x$ ?

anonymous · Answer

that takes care of the vertical asymptotes. but for horizontal, it seems that function converges to y=1 as x=infty

tkhunny · Answer

Not sure where that x came from.  Is y = 1 and "asymptote"?

goformit100 · Answer

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anonymous · Answer

I meant, $y=1$ is the asymptote.

tkhunny · Answer

No objection.  Just a definition check.

Do we get to cross it infinitely many times and still call it an asymptote?

anonymous · Answer

yes. 
Asymptote of a function is a straight line to which that function tends to converge at infinity. 
can be horizontal, vertical or with a finite slope.