Key Idea 32 gives the nth term of the Taylor series of common func􏰀ons. In Exercises 3 – 6, verify the formula given in the Key Idea by finding the first few terms of the Taylor series of the given functi􏰀on and idtifying a ptarteeny. \(f(x)=sinx;c=0\)

\(sinx=∑n=0∞(−1)nx2n+1(2n+1)!\)

\(\begin{equation} f(x) = 1 * \frac{x^{1}}{(1)!} + -1 * \frac{x^{3}}{(3)!} + 1 * \frac{x^{5}}{(5)!} + -1 * \frac{x^{7}}{(7)!} + ... \end{equation}\)

\(f(x)=x−x36+x5120−x75040+...t\)

taylor(sin, 0, 7)
## [1] -0.0001983869  0.0000000000  0.0083332754  0.0000000000 -0.1666666439
## [6]  0.0000000000  1.0000000000  0.0000000000