Use Exercise 68 to show that for x ≥ 0 and all n,

Sketch the graphs of y = e^x, y = T₁(x), and y = T₂(x) on the same coordinate axes. Does this inequality remain true for x

Data From Exercise 68

Let x ≥ 0 and assume that ƒ⁽ⁿ⁺¹⁾(t) ≥ 0 for 0 ≤ t ≤ x. Use Taylor’s Theorem to show that the nth Maclaurin polynomial T_n satisfies T_n(x) ≤ ƒ(x), for all x ≥ 0

Transcribed Image Text:

et 21+x+ 2! th n!