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I am having difficulties trying to adopt the formal definition of Limits as x -> infinity. I will simply try to explain my problem using an example.

Formal definition requires me to find a general equation M, in terms of e. How can I do that with these type of questions?Code (Text):

The Formal Definition of Limits as x -> infinity is as follows:

Limit of f(x) as x -> infinity = L, iff we can find M such that

x > M forces absolute value of f(x) - L < e.

note: e = epsilon, M = a function of epsilon

Question:

Find as x -> infinity, the limit of: and prove using the Formal Definition.

f(x) = (sin 3x) / (x^2 + 4), the answer is 0.

Here are some I can't do:

Code (Text):

f(x) = (x + 3) / (x^2 - 3)

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# Formal Definition of Limits, as x -> infinity

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