Let f and g be functions satisfying the following conditions:

(a) f (0) = 1, (b) f' (x) = g (x), g' (x) = f (x), (c) g (0) = 0.

Estimate f (1) to three decimal places

Question

Mathematics

Nora Romero

15 February, 01:45

Let f and g be functions satisfying the following conditions:

(a) f (0) = 1, (b) f' (x) = g (x), g' (x) = f (x), (c) g (0) = 0.

Estimate f (1) to three decimal places

+3

Answers (1)

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Nadia Norris · Answer 1

1

Step-by-step explanation:

Linearization equation: L (x) = f (a) + f′ (a) (x-a)

L (1) = f (0) + f' (0) (1-0)

L (1) = 1 + 0 (1) = 1

g (0) is equal to f' (0), so I substituted g (0) for f' (0) in the Linearization equation

This estimation is extremely off due to how big the change in x is.

Let f and g be functions satisfying the following conditions:(a) f (0) = 1, (b) f' (x) = g (x), g' (x) = f (x), (c) g (0) = 0.Estimate f (1) to three decimal places

Let f and g be functions satisfying the following conditions:

(a) f (0) = 1, (b) f' (x) = g (x), g' (x) = f (x), (c) g (0) = 0.

Estimate f (1) to three decimal places