Question 53515
List the intercepts and test for symmetry.
y = (x^2 - 5)/2x^3
at x=0,we have y undefined...tends to infinity..hence the curve goes parallel to y axis approaching it at infinity as x tends to zero
at y=0,we have
x^2=5....x=+sqrt(5) and -sqrt(5) which are the x intercepts.
we find that by replacing x with -x and y with -y,we get same eqn.
-y = {(-x)^2-5}/2(-x)^3
y=(x^2-5)/2x^3 which is same eqn. as the given one.
hence the graph is symmetric about origin