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Determine $\lim_{x \rightarrow \infty}\dfrac{4x^3+x^2}{x^3+3}$
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As you can see the answer is in the provided picture. The final step cutoff at the bottom says: (4+0)\(1+0) = 4\1 = 4.

Note that this numbers of steps is not necessary in most cases. It is simply to show the method in painstaking detail.

As you can see, we begin by dividing both numerator and denominator by x^3. This reduces all terms to either constants or to terms with powers of x in the denominator. Limits for both of these kinds of terms are easy to evaluate.

Then the quotient law for limits is used (limit of quotient is equal to quotient of limits)

Then the sum law for limits is used (limit of sum is equal to sum of limits)

Finally, the limits are evaluated.

When it comes to tests most of the time I would suggest simply putting in the dividing step, the expression after the division, then (4+0)\(1+0) = 4\1 = 4 in order to save time. The rest of the steps will almost certainly be considered trivial enough that they do no need to be provided.

by Wooden Status (248 points)

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