- #1

mileena

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## Homework Statement

lim x→∞

##\frac{7x^2 + x + 11}{4 - x}##

## Homework Equations

## The Attempt at a Solution

I am sorry I am posting so much. But I think I have learned two different ways to compute limits at infinity of functions: one by the math lab tutor and another by the professor, but I am not sure. Sometimes they don't work.

The tutor said the denominator always controls. So always divide both the numerator and denominator by the largest degree variable in the denominator.

And my professor said that if the numerator has the highest power, the limit is ∞. If the denominator has the highest power, the limit is 0. And if the highest powers in the numerator and denominator equal, divide by the highest power.

So here is the problem:

lim x→∞

##\frac{7^2 + x + 11}{4 - x}##

It's too complicated for me now to learn to use LaTeX to write a fraction within a fraction, since I have to leave in 45 minutes and I am scrambling, but basically I divided each term above by

*x*and not x

^{2}(since the math lab tutor said the denominator always controls) and I got:

##\frac{∞ + 1 + 0}{0 - 1}## =

∞/-1 =

-∞

But the correct answer, according to my professor, is ∞.

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