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zonk

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I am currently reading Apostol volume 1, and I'm having trouble understanding little-o notation. I have searched the web for free resources, but can't find any. I don't quite understand his proof for theorem 7.8.e, and I don't understand his examples.

For instance, why does [itex]\frac{1}{1 + g(x)} = 1 - g(x) + g(x)\frac{g(x)}{1 + g(x)} = 1+ g(x) + o(g(x))[/itex] as g(x) approaches 0?

Also for his example, why does [itex]o(-\frac{1}{2}x^2 + o(x^3)) = o(x^2)[/itex]?

Anyone know of any free resource that explains this lucidly?

For instance, why does [itex]\frac{1}{1 + g(x)} = 1 - g(x) + g(x)\frac{g(x)}{1 + g(x)} = 1+ g(x) + o(g(x))[/itex] as g(x) approaches 0?

Also for his example, why does [itex]o(-\frac{1}{2}x^2 + o(x^3)) = o(x^2)[/itex]?

Anyone know of any free resource that explains this lucidly?

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