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Consider the equation

ε x^3 + x^2 - x - 6 = 0 ,ε > 0. (1)

1. Apply a naive regular perturbation of the form

x~[itex]^{0}_{∞}Ʃ[/itex] x_{n}ε^{n}as ε→0^{+}

do derive a three-term approximation to the solutions of (1).

2. The above perturbation expansion should only give you an approximation for 2 of the roots.

Apply a leading order balance argument to device suitable expansions for the other root, again

in the limit ε → 0^{+}. Again, derive a three-term approximation this third case.

3. Solve (1) numerically for ε = 0.01 ?

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# Naive regular perturbation

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