Asymptotes

Asymptote is a straight line at a finite distance from the origin is said to be asymptote of the curve y=f(x)

if the perpendicular distance from the point P on the curve from the line tends to zero when x or y both tends to infinity

a straight line A is called asymptote of the curve if the distance δ from the variable;e point of M of the curve to this straight line approaches to zero as position tends to infinity as shown

Mathematically

let y=f(x) be the curve and let (x,y) be the point on it

Tangent at (x,y) is given by

Y-y=dy/dx(X-x)

Y=dy/dx.X+(Y-xdy/dx)

if the asymptote exist as x→∞

dy/dx and (y-xdy/dx)→ finite limit say slope m and intercept C

dy/dx→m

(y-xdy/dx)→C

The equation will reduce to Y=mX+C

There are various type of asymptotes

a) asymptote parallel to the x-axis

a) asymptote parallel to the y-axis

c)asymptotesof algebric curves or oblique asymptotes

d)Asymptote by inspection

e)intersection of the curve and its asymptotes

f)Asymptotes by expansion

g)the position of the curve concerning asymptote