f x x a 0 n 3 0 x 0 2 Exercise a Approximate f by a Taylor

Last updated: 5/25/2023

f x x a 0 n 3 0 x 0 2 Exercise a Approximate f by a Taylor polynomial with degree n at the number a Step 1 The Taylor polynomial with degree n 3 is The function f x 2x has derivatives Step 2 T3 x f a f a x a f a x a f a x a 21 31 Step 3 f x H f x H Therefore T x 4x With a 0 f 0 1 16x 4 64x 48r Submit Skip you cannot come back 4r 16x 4 1 f 0 0 Step 1 If Ir 4 x M then we know that M R x 64 48 Tx9 x and Je x 0 F 0 4 Exercise b Use Taylor s Inequality to estimate the accuracy of the approximation fx T x when x lies in the given interval and f 0 0