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

question 34

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) \(R(x)=\frac{120 x^{5}-24 x^{3}+x}{30 x^{4}-60 x^{2}+120}\)

---

Definitions:

Developmental Stages

Distinct phases of growth and development that a person passes through from infancy to adulthood, often characterized by specific milestones or abilities.

Life Cycle

A series of stages through which a living organism passes, from its birth to reproduction and eventually death.

Developmental Approach

Branch of social sciences concerned with interaction between physical, psychological, and social processes and with stages of growth from birth to old age.

Herman Feifel

A pioneering psychologist known for his groundbreaking work on the psychology of death.