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Ksenya-84 [330]
3 years ago
10

The side length of a square ice cube is claimed to be 1.0 inches, correct to within 0.001 inch. Use linear approximation to esti

mate the resulting error, measured in squared inches, in the surface area of the ice cube.
Mathematics
1 answer:
Olenka [21]3 years ago
3 0

Answer:

0.012

Step-by-step explanation:

Linear approximation says that,

f(x) \approx f(x_o)+f'(x_o)(x-x_o)

For a cube the surface area is 6x^2.

So the side is 1.0 inch in, the surface area is =6\times1^2 = 6 square inches.  

In Linear approximation means you ignore the term x_o^2 , if x_o is a small number, because then x_o^2 will be a very smalle number and that does not contribute much to the error.  

So the surface area is approximately,

6x^2=6x_o^2+12x_o(x-x_o)

So here, x=1.001, x_o=0.001

The error in the area is approximately,

12 \times 0.001=0.012

So the error is 0.012.


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