Suppose that the demand equation for a certain item is 1p+1x2−160=0. evaluate the elasticity at 65:

Price elasticity is defined as [tex]\frac{\Delta(quantity)}{\Delta(price)}[/tex].

Here, the question has omitted to define variables, so we will ASSUME
p=price
x=variable,
and we're given
p+x^2-160=0

We calculate
[tex]\delta{x}/\delta{p}[/tex] by implicit differentiation with respect to p:
1+2x (dx/dp)=0
=>
E(x)=(dx/dp)=-1/(2x)

Therefore the price elasticity at x=65 is
E(65)=1/(2*65) =-1/130 (approximately -0.00769)