1. 12. Let f : I → R, where I is an open interval containing the point x 0 . Let n ∈ N, suppose that f is n-times differentiable at x0, and let pn be the nth Taylor polynomial for f at x = x 0 . (a)...

1. 12. Let f : I → R, where I is an open interval containing the point x₀. Let n ∈ N, suppose that f is n-times differentiable at x0, and let pn be the nth Taylor polynomial for f at x = x₀.

(a) Apply l’Hospital’s rule n – 1 times and then use the definition of f⁽ⁿ⁾
(x₀) to show that

(b) Why can’t we just apply l’Hospital’s rule n times in establishing the limit in part (a)?