Individual Post – Test #2 Solution: Taylor Series

Problem #7 is to work with Taylor Series with given f(x) = e^x centered at a =4 to find the first 5 non-zero terms. The equation e^x is constant and cannot be derived interchangeably. Written as Taylor Polynomials, the polynomial formula is e^xxⁿ/n! so e^x = the sum of e^xxⁿ/n! from n = 0 to infinity. To find the limit in determining whether the series diverges or converges, the sum is to be rewritten as a limit to apply the ratio test. By the ratio test, P = 0 so the series diverges and accordingly, the radius of convergence R = infinity.