Answer
a) The proof is below.
b) $2b(\sqrt{x_2})$
Work Step by Step
a) We know that work is equal to the integral of the force with respect to x. Thus:
$W = \int_{x_1}^{x_2} bx^{-.5}dx \\ W = 2b\sqrt{x}|_{x_1}^{x_2}= 2b(\sqrt{x_2}-\sqrt{x_1})$
When $x_1$ equals 0, this becomes: $ 2b(\sqrt{x_2})$, which is a finite value.
b) As we found above, the work done as the limit of x approaches 0 is: $ 2b(\sqrt{x_2})$
