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vodka [1.7K]
2 years ago
10

[25 POINTS] The approximate change in the value of f(x) = sqrt(2(x-1)) at x = 3 using differentials with dx = 0.01 is

Mathematics
1 answer:
otez555 [7]2 years ago
8 0

Answer:

\frac{1}{200}

Step-by-step explanation:

<u>Find the derivative of the function when x=3</u>

<u />y=\sqrt{2(x-1)}

\frac{dy}{dx}=\frac{1}{\sqrt{2(x-1)}}

\frac{dy}{dx}=\frac{1}{\sqrt{2(3-1)}}

\frac{dy}{dx}=\frac{1}{\sqrt{2(2)}}

\frac{dy}{dx}=\frac{1}{\sqrt{4}}

\frac{dy}{dx}=\frac{1}{2}

Since the change in the value of the function is dy and we know that the change in x is dx=0.01, then we have:

\frac{dy}{dx}=\frac{1}{2}

dy=\frac{1}{2}dx

dy=\frac{1}{2}(0.01)

dy=\frac{1}{200}

Therefore, the 2nd option is correct

<u />

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