Question

Taylor Polynomials for cos(x) for x near π. The Taylor polynomial for cos(x) of degree 4 near π can be found by using the Taylor series expansion of cos(x) around π, which is P4(x)=1−2!1(x−π)2+4!1(x−π)4.

Answer 1

The Taylor polynomial for cos(x) of degree 4 near π can be found by using the Taylor series expansion of cos(x) around π. It is given by P4(x)=1−2!1(x−π)2+4!1(x−π)4.

Step-by-step explanation:

The Taylor polynomial for cos(x) of degree 4 near π can be found by using the Taylor series expansion of cos(x) around π, which is P4(x)=1−2!1(x−π)2+4!1(x−π)4. The Taylor series expansion of a function allows us to approximate the function with a polynomial. In this case, the Taylor polynomial for cos(x) gives us an approximation of the cosine function near π, up to the 4th degree term.