Mathematics

Problem

Determine the algebraic rewrite that most directly facilitates evaluating the limit

\displaystyle\lim_{x\to 0}\frac{1-\cos x}{x^{2}}

. Which of the following substitutions is MOST appropriate? a) Rewrite

1-\cos x

\sin^{2}x

b) Rewrite

1-\cos x

2\sin^{2}\dfrac{x}{2}

c) Rewrite

1-\cos x

2\sin^{2}x

d) Rewrite

1-\cos x

\dfrac{x^{2}}{2}