Estimating (16.1)1/4 using Taylor's Expansion at x=16

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SUMMARY

The discussion focuses on estimating (16.1)^(1/4) using Taylor's expansion of the function f(x) = x^(1/4) around x = 16. The Taylor series expansion derived is 2 + (1/32)(x - 16) - (3/320)(x - 16)^2 + (7/262144)(x - 16)^3. To estimate (16.1)^(1/4), one simply substitutes 16.1 into the Taylor expansion and verifies the result using a calculator for accuracy.

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Homework Statement



Use the taylor's expansion of f(x)= x1/4 about x= 16 to estimate (16.1)1/4

Homework Equations


Taylors formula: f(a) + f'(a) (x-a) + (f''(a)/2!) (x-a)2+...

The Attempt at a Solution



Ok I have calculate the taylor expansion to be: 2 + (1/32) (x-16)-(3/320) (x-16)2+ (7/262144) (x-16)3

I just don't know what to do after this - do i just substitute 16.1 into the value for x in the taylor expansion I have just found?
 
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yep - then check whether you're close with a caclulator
 
thanks it works
 

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