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Find the 4th root of 82 by using differentials.

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Calculator: 3.009217

 

asked Jul 19, 2014 in PRECALCULUS by anonymous

1 Answer

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y = f(x) = X1/4.
dy/dx = 1 /(4 X3/4)
dy = 1 / (4 X3/4) dx --------------- (1)

dy is the change in y and dx is the change in x.

14 = 1
24 = 16
34 =81

So 81= 34 is close to 82.

Let x = 81

dx = 82-81 =1

Substitute 81 for x and 1 for dx in equuation (1).
dy = 1 / (4 X3/4) dx

dy = 1 / (4 (81)3/4) dx
     = 1 / (4 (34)3/4) (1)
     = 1 / (4 (33))
     = 1 / ((4)(27))
     = 1 / 108
dy = 0.00926

Calculate the number
y + dy = (X1/4) + (0.00926)

            =((81)1/4) + (0.00926)

            =((34)1/4) + (0.00926)

            = 3 + 0.00926

            = 3.00926

Therefore, the approximate fourth root of 26 is 3.00926.

answered Jul 19, 2014 by bradely Mentor

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