College Math CLEP Prep Practice Exam

What is the limit of (2x^2+4x-3)/(x+2) as x approaches infinity?

1. Infinity

2. -3

3. 2

4. Undefined

The correct answer is: 2

As x approaches infinity, the highest degree term (2x^2) becomes increasingly larger in comparison to the rest of the polynomial. Essentially, the other terms become insignificant in relation to the highest degree term. Therefore, the limit approaches the coefficient of the highest degree term, which in this case is 2. Infinity (option A) is incorrect because while the numerator does approach infinity, the denominator also approaches infinity, resulting in a limit that can be a finite number. -3 (option B) is incorrect because while the constant term -3 does not change, it becomes insignificant in comparison to the increasing value of the highest degree term. Undefined (option D) is incorrect because the limit does exist and can be calculated.