In Exercises 7 – 12, find a formula for the n th term of the Taylor series of f(x), centered at c, by finding the coefficients of the first few powers of x and looking for a paƩern. (The formulas for several of these are found in Key Idea 8.8.1; show work verifying these formula.)
Chapter 8.8 Exercises 12
f(x)=1/x;c=1
f′(x)=−1/x^2 f′′(x)=2/x^3 f′′′(x)=−6/x^4 f(4)(x)=24/x5
Now we can solve for f^n
f(n)(x)=((−1)(n+1))(1/x^n) f(n)(c)=(−1)(n+1)