Chapter 2.2, Problem 81E

Shock waves arise in many physical applications, ranging from supernovas to detonation waves. A graph of the density of a shock wave with respect to distance, x, is shown here. We are mainly interested in the location of the front of the shock, labeled x_SFin the diagram.

a. Evaluate $\underset{x\to x_{SF}{}^{+}}{\lim }\rho \left(x\right)$

b. Evaluate $\underset{x\to x_{SF}{}^{-}}{\lim }\rho \left(x\right)$

c. Evaluate $\underset{x\to x_{SF}}{\lim }\rho \left(x\right)$ . Explain the physical meanings behind your answer.