APFIVE Limit of a Rational Function at Infinity
A researcher evaluates $$\lim_{x\to \infty} \frac{3*x^2 - 2*x + 1}{5*x^2 + 4}$$. They incorrectly divide the numerator and denominator by $$x$$ instead of $$x^2$$ and, through erroneous cancellation, conclude that the limit is $$\frac{3}{5}$$. Identify the error in the process.
A
The error is in dividing by the wrong power of $$x$$; since the highest power in the expression is $$x^2$$, both numerator and denominator should be divided by $$x^2$$ to simplify correctly.
B
The mistake is in expanding the polynomials rather than factoring them first.
C
The error is in using polynomial long division instead of direct cancellation.
D
There is no mistake because the limit still evaluates to $$\frac{3}{5}$$.
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