What Happens to the Limit of $|x|^2$ as $n$ Approaches Infinity?

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SUMMARY

The limit of the expression $$\lim_{{n}\to{\infty}} \frac{|x|^2}{(2n + 3)(2n + 2)}$$ approaches 0 for finite values of $x$. When $x$ approaches infinity, the expression becomes an indeterminate form. However, if $x$ and $n$ are treated as the same variable, the limit can be evaluated using the principle that the limit of the ratio of two polynomials of the same degree equals the ratio of their leading coefficients.

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I have

$$\lim_{{n}\to{\infty}} \frac{|x|^2}{(2n + 3)(2n + 2)}$$

I can see that for smaller values of $x$ the limit is 0, but what if $x$ equals infinity, wouldn't that be an indeterminate form?
 
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If $x$ and $n$ is the same variable, then use the fact that the limit of the ratio of two polynomials of the same degree when the argument tends to +infinity equals the ratio of their leading coefficients.
 

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