The goal of Taylor approximation is to approximate a function f(x) with a polynomial of degree n centered at c: Tn(x) = ao+a₁(x-c) + a₂(x-c)²+...+an(x-c)". f(k) (c) k! In this problem, you will show that a = assuming that f(k) (c) = T() (c), where k = 0,1,2, - - -. (a) If T₁ (x) = a + a₁(x − c) + a₂(x − c)² + + an(rc)", what is T₁(c)? (b) What are T (c), T (c) and T³) (c)? (c) Do you see a pattern? What is T) (c)? (d) Using the equality: f(k) (c) = T(k) (c) and the result in (c), show that a = f(k) (c) k!

The goal of Taylor approximation is to approximate a function f(x) with a polynomial of degree n centered at c: Tn(x) = ao+a₁(x-c) + a₂(x-c)²+...+an(x-c)". f(k) (c) k! In this problem, you will show that a = assuming that f(k) (c) = T() (c), where k = 0,1,2, - - -. (a) If T₁ (x) = a + a₁(x − c) + a₂(x − c)² + + an(rc)", what is T₁(c)? (b) What are T (c), T (c) and T³) (c)? (c) Do you see a pattern? What is T) (c)? (d) Using the equality: f(k) (c) = T(k) (c) and the result in (c), show that a = f(k) (c) k!

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter14: Discrete Dynamical Systems

Section14.3: Determining Stability

Problem 1E

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