Question

Consider the function f(x) = ln(sin(x)). Expand f(x+h) using Taylor's series. In this context, the correct statement(s) is/are

• A. Second term in the Taylor's series i.e., the term which includes his: h. ln(sin(x))
• B. First term is ln(sin(x))
• C. Third term in the Taylor's series i.e., the term which includes $h^2$ is: $\frac{-h^2}{2(sin(x))^2}$
• D. Third term in the Taylor's series i.e., the term which includes $h^2$ is: $\frac{2h^2}{(sin(x))^2}$

Answer 1

Answer: (B), (C)

First term is ln(sin(x))

Answer 2

The correct answer is (B and C) : First term is ln(sin(x)) AND Third term in the Taylor's series i.e., the term which includes $h^2$ is: $\frac{-h^2}{2(sin(x))^2}$