7: The denominator goes to infinity, in the numerator there is the indeterminate difference ∞ − ∞. In fact, in the numerator the term 3ⁿ eventually prevails, so the ratio is of the type. However, l'Hospital is not possible, since −3 < 0 and so (−3)ⁿ cannot be turned into a function. So the only reasonable way is to find dominant terms and factor out.

First rewrite the expression to be able to identify the dominant term.

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