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PCAT Quantitative Reasoning – Limit as X Approaches Infinity

Find the limit of f(x) = –4x2 + 9x + 1 as x approaches infinity.

A. –∞
B. 0
C. ∞
D. This limit is undefined.

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A is correct. To solve for this limit, we will need to plug ∞ in for x in the function. However, note that the term –4x2 is going to change much more rapidly than the term 9x for any given value of x. In other words, the –4x2 term is going to make the result much smaller or more negative than 9x can counteract as x grows larger. Therefore, we really ought to solve for:

Now let’s plug in ∞ for x:

This means that as x gets larger and larger as it approaches infinity, the y value will become smaller and smaller (more negative), approaching negative infinity.

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