Chapter 2 | Limits
159
81. 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 SF in the diagram.
ρ ( x ).
lim x → x SF + lim x → x SF −
a. Evaluate
ρ ( x ).
b. Evaluate
ρ ( x ). Explain the physical
lim x
c. Evaluate
→ x SF
meanings behind your answers. 82. A track coach uses a camera with a fast shutter to estimate the position of a runner with respect to time. A table of the values of position of the athlete versus time is given here, where x is the position in meters of the runner and t is time in seconds. What is lim t →2 x ( t )? What does it mean physically? t (sec) x (m)
1.75
4.5
1.95
6.1
1.99
6.42
2.01
6.58
2.05
6.9
2.25
8.5
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