## ASYMPTOTE

Posted by tendstoinfinity on December 2, 2010

**While teaching curve tracing I always found if the students doesn’t have the idea of asymptotes they are not able to understand the whole idea of curve tracing that is why this topic **

**Asymptotes: **By def.,** ***asymptote is that st. line which meets the curve at two points at infinity. *Now the method to find the equation of asymptote

**Method 1:**

- If at least one of or then
*x = a*is vertical asymptote. The curve lies on the right or left of the asymptote according as the case. - If then
*y = A*is horizontal asymptote. - If and exist then
*y = mx + c*is an asymptote.

find the asymptote of*Example*

It is clear that (by using L’hospital rule) (what about ?)

Hence *x = 0* is vertical asymptote.

There is no vertical asymptotes

Again for oblique asymptote

and

c= (expanding )

hence *y =x + 1* is an asymptote.

What about the annexed graph ?

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