Find the linear approximation of the function f(x) = √4-x at a = 0 and use it to approximate the numbers……?

Find the linear approximation of the function f(x) = √4-x at a = 0 and use it to approximate the numbers……?

Find the linear approximation of the function f(x) = √4-x at a = 0 and use it to approximate the numbers √3.9 and √3.99.

Update:

f(x) = √(4-x)

Answer:

f'(x) = -1 / [ 2√(4-x) ]

At a=0:

f(0) = 2

f'(0) = -1/4

So the linear approximation is

f(x) ≈ 2 – (1/4)x

√3.9 = f(0.1) ≈ 2 – 0.025 = 1.975

√3.99 = f(0.01) ≈ 2 – 0.0025 = 1.9975

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