PCAT Quantitative Reasoning – Limit as X Approaches Infinity
 by
 Apr 19, 2018
 PCAT Question of the Day
Find the limit of f(x) = –4x^{2} + 9x + 1 as x approaches infinity.
A. –∞
B. 0
C. ∞
D. This limit is undefined.
Click for Explanation
A is correct. To solve for this limit, we will need to plug ∞ in for x in the function. However, note that the term –4x^{2} is going to change much more rapidly than the term 9x for any given value of x. In other words, the –4x^{2} 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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