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blondesaturn
26.09.2019 •
Mathematics
Find the linear approximation of the function f(x) = 4 − x at a = 0. l(x) = use l(x) to approximate the numbers 3.9 and 3.99 . (round your answers to four decimal places.) 3.9 ≈ 3.99 ≈ illustrate by graphing f and the tangent line.
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Ответ:
The linear approximate value of f(x) ≈ 20
Step-by-step explanation:
The linear approximation of a function f(x) is given by
f(x + Δx) = f(x) + f'(x) × Δx
It leverages the tangent line to approximate values of a function close to a particular point.
Using the Taylor form:
f(x) = f(a) + (x - a) × f'(a)
Now,
From the given question:
f(x) = 4 - x
On differentiate, we get
f'(x) = 4
And
At a = 0
f(0) = 4 - 0 = 4
f'(0) = 4
Therefore,
f(x) = f(a) + (x - a) × f'(a)
f(x) = f(0) + (x - 0) × f'(0)
f(x) = 4 + (x) × 4 = 4 + 4x
∴ at x = 3.9
f(x) = 4 + 4 × 3.9 = 19.6
At x = 3.99
f(x) = 4 + 4 × 3.99 = 19.96
Hence, the linear approximation of the function f(x) is
f(x) ≈ 20
Ответ:
The full length of the journey = 3150 miles
on the first day they completed = 567 miles
suppose 567 is x% of 3150 So
3150 x = 567
100
let us multiply both sides by 100 and divide both sides by 3150
x= 567 * 100
3150
x= 18
Answer is 18 %