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liraira [26]
3 years ago
5

The sum of three consecutive odd integers is 17 less than four times the smallest integer

Mathematics
1 answer:
Lilit [14]3 years ago
4 0

x = smallest \: int \\ x + (x + 2) + (x + 4) = 4x - 17 \\ 3x + 6 = 4x - 17 \\ 23 = x \\ numbers = 23 \: 25 \: 27
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Answer:

L(x)=\frac{1}{8}x+2\\ L(16.4)=4.05

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The equation for a tangent line of f(x) in the point (a,f(a)) can be calculated as:

L(x) = f(a) + f'(a)(x-a)

Where L(x) is also call a linear approximation and f'(a) is the value of the derivative of f(x) in (a,f(a)).

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Then, to find the linear approximation we are going to use the point (16, f(16)). So a is 16 and f(a) and f'(a) are calculated as:

f(16)=\sqrt{16}=4\\f'(16)=\frac{1}{2\sqrt{16} }=\frac{1}{8}

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L(16.4)=\frac{1}{8}(16.4)+2\\ L(16.4)=4.05

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