How do you find the vertical, horizontal and slant asymptotes of: f(x) = x/ sinx?
1 Answer
Aug 6, 2016
It has a hole at
Explanation:
Vertical asymptotes will occur where the denominator is zero and the numerator non-zero.
sin x = 0 if and only ifx = n pi for somen in ZZ
Hence
lim_(x->0) x/(sin x) = 1
f(2n pi+pi/2) = 2n pi+pi/2 -> +oo asn -> +oo
f(2n pi+pi/2) = 2n pi+pi/2 -> -oo asn -> -oo
f(2n pi+(3pi)/2) = -(2n pi+(3pi)/2) -> -oo asn -> +oo
f(2n pi+(3pi)/2) = -(2n pi+(3pi)/2) -> +oo asn -> -oo