Second Order Approximation for a Polynomial if I have an expression: L = 12

Desirae Washington 2022-07-02 Answered
Second Order Approximation for a Polynomial
if I have an expression: L = 12 a 3 d 3 4 w a 3 d 2 + 16 a 2 d 2 4 w a 2 d + 6 a d + 1 12 a 3 d 3 4 w a 3 d 2 4 a 2 w d + 16 a 2 d 2 + 7 a d a w + 1 what is the second order approximation in d w ?
I know that ( d w ) 2 can be ignored but what about d 2 w 3 . At this instant (without knowing the actual values of d wrt w) can we ignore this too? What about if we have (d/w=0.001)? Also how would the first order approximation in (d/w) be different in both cases?
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Answers (1)

jugf5
Answered 2022-07-03 Author has 18 answers
If the expression's numerator and denominator were both homogenous in d and w (for example, d + w d 2 w 2 ) then it would be meaningful to ask for an n-th order expansion in d w . The expression given is not homogenous in this sense, so approximation in d w without further specification (such as d w 1 ; d 1 is not a well-posed question.

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