If length of perpendicular drawn from points of a curve to a straight line approaches zero along an infinite branch of the curve, the line is said to be an asymptote to the curve. For example, \( y \)-axis is an asymptote to \( y=\ell \ln \& x \)-axis is an asymptote to \( y=e^{-x} \).
Asymptotes parallel to \( \mathrm{x} \)-axis :
If \( \lim _{x \rightarrow \infty} f(x)=e \) (a finite number) then \( y=e \) is an asymptote to \( y=f(x) \). Similarly if \( \lim _{x \rightarrow-\infty} f(x)=\alpha \), then \( y=\alpha \) is also an asymptote.
Asymptotes parallel to \( y \)-axis :
If \( \lim _{x \rightarrow a} f(x)=\infty \) or \( \lim _{x \rightarrow a} f(x)=-\infty \), then \( x=a \) is an asymptote to \( y=f(x) \).
Number of asymptotes parallel to co-ordinate axes for the function \( f(x)=\frac{(x+1)(x+2)}{(x-1)(x-2)} \) is equal to :
(A) 1
(B) 2
(C) 3
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