Use the Taylor Polynomials for the Sine and Cosine Functions $R(x)=\frac{x^{5}+24 x^{4}-120 x^{3}}{x^{4}-6 x^{2}+120}$

Multiple Choice

Use the Taylor polynomials for the sine and cosine functions to find a rational function with a degree 5 numerator and no fractional coefficients that approximates the tangent function near 0.

A) $R(x) =\frac{x^{5}+24 x^{4}-120 x^{3}}{x^{4}-6 x^{2}+120}$
B) $R(x) =\frac{x^{5}-20 x^{3}+120 x}{5 x^{4}-60 x^{2}+120}$
C) $R(x) =\frac{30 x^{4}-6 x^{2}+120}{-120 x^{3}+x^{5}}$
D) $R(x) =\frac{120 x^{5}-24 x^{3}+x}{30 x^{4}-60 x^{2}+120}$