Taylor Polynomials Find the Taylor polynomial of degree n, centered at the number a, for the function defined by the given equation. You will need to use your higher order thinking skills for the last five! 1. f(x) = sin(x); a = ";n = 3 2. f (x) = tan(x) ; a = 0;n = 3 3. f(x) = In(x); a = 1;n = 3 4. f (x) = Vx;a = 4;n = 4 5. f(x) = In(cos(x)) ; a = ";n = 3 6. f (x) = ex; a =0;n = 3 7. f(x) = (1 +x) /2; a= 0;n = 3 8. f(x) = (1 -x) /2;a = 0;n = 3 9. Compute the value of e correct to five decimal places, and prove your answer has the required accuracy. 10. Use the Tavlor polynomial in problem 4 to compute v5 accurate to as many places compute In(1.2), accurate to four decimal places. 12. Use a Taylor polynomial centered at 0 for the function f (x) = In(_) to compute In(1.2), accurate to four decimal places. Compare the computation with that in problem 11. 13. Show that the formula (1 + x) /2 ~ 1 + 5 x is accurate to three decimal places if -0.03 S x SO