horizontal and vertical asymptotes of y=x/sinx

Question

find all horizontal and vertical asymptotes of 

y=x/sinx

 

vertical asymptotes: if i set denominator to 0, then sinx=0 and x= 0 or npi? 

 

horizontal asymptotes: i have to find the limit of the function as x approaches positive and negative infinity? 

i am unsure how to do this. when graphed, it looks like this function has an oblique asymptote. 

Answer 1

vertical asymptotes: if i set denominator to 0, then sinx=0 and x= 0 or npi?

CORRECT...in fact, x = n(pi) is sufficient because n can be an integer, including zero.

 

As x→ ±infinity, y also approaches infinity (wildly) and perhaps you should use a graphing calculator (not in Degree Mode) to show this function's behavior. It's not H.A. behavior because that would result in y → a constant, as x increases without bound.

 

In the vicinity of zero, y →  1 because the limit of x/sinx is 1, a well known result from early Calculus.