Chapter 13.2, Problem 38E

To determine

To find: the value of limit.

Answer to Problem 38E

The value of limit is $0$ .

Explanation of Solution

Given information:

The equation is $L=L_0\sqrt{1-\frac{v^2}{c^2}}$ .

Calculation: to find the limit, first substitute and then simplify,

  $\begin{array}{l}\underset{v\to c^{-}}{\lim }L=\underset{v\to c^{-}}{\lim }{L}_0\sqrt{1-\frac{v^2}{c^2}}\\ \underset{v\to c^{-}}{\lim }L=\underset{v\to c^{-}}{\lim }{L}_0\sqrt{1-\frac{c^2}{c^2}}\text{ [substitute]}\\ \underset{v\to c^{-}}{\lim }L=0\text{ [simplify]}\end{array}$

Thus, the value of limit is $0$ .