Let
S(x)=x2sinx1+2x−1−x,
where x is measured in radians.
a. Algebraically transform S(x) into a form that separates the radical expression from the trigonometric factor, so that each may be analyzed by a standard limit theorem. Display every algebraic manipulation.
b. Determine x→0limS(x). Provide a justification that cites any standard limits or theorems you invoke.