For the demand function $q=D(x)=\frac{300}{x}$, find the following.
a) The elasticity
b) The elasticity at $x=5$, stating whether the demand is elastic, inelastic, or has unit elasticity
c) The value(s) of $x$ for which total revenue is a maximum (assume that $x$ is in dollars)
a) Find the equation for elasticity.
$$E(x)=$$

Step 1 ：The elasticity of demand is a measure of how much the quantity demanded of a good responds to a change in the price of that good. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. In this case, the demand function is given by $q=D(x)=\frac{300}{x}$, where $x$ is the price.

Step 2 ：The elasticity of demand is given by the formula: $E(x)=x\cdot \frac{D^{\prime }(x)}{D(x)}$, where $D^{\prime }(x)$ is the derivative of the demand function with respect to $x$. So, the first step is to find the derivative of the demand function.

Step 3 ：The derivative of the demand function $D(x)$ is $D^{\prime }(x)=-\frac{300}{x^2}$.

Step 4 ：Now, we can substitute $D(x)$ and $D^{\prime }(x)$ into the elasticity formula to find the elasticity of demand.

Step 5 ：The elasticity of demand $E(x)$ is $-1$. This means that the percentage change in quantity demanded is equal to the percentage change in price, but in the opposite direction.

Step 6 ：Final Answer: The elasticity of demand is $\boxed{{\displaystyle -1}}$.