Question

I need help with this long term behavior math problem.
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Answer 1

For large |x| this tends to 3/x, which goes to zero, so a horizontal asymptote at y=0.

Answer 2

b.

Explanation:

The slant asymptote will only exist if the degree of the top is one more than the degree of the bottom.

Here it is the other way around.

The degree of the top is 2.

The degree of the bottom is 3.

So there is no slant asymptote.

There will be a horizontal asymptote when the degree of the bottom is more than or equal to the degree of the top.

When the degrees are equal, the horizontal asymptote will be

y=(leading coefficient of top)/(leading coefficient of bottom).

Since the degree is more on bottom than the degree on top, then the horizontal asymptote is y=0.

The answer is b, then.