Limit of a Rational Function at Infinity

Question

When evaluating $$\lim_{x	o \infty} \frac{3x^2 - 2x + 1}{5x^2 + 4}$$, a student's procedure involves dividing the numerator and denominator by $$x$$. This step, combined with another error, leads to the correct answer of $$\frac{3}{5}$$. Which statement describes the primary flaw in the student's method?

Accepted Answer

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.

Answer

The mistake is in expanding the polynomials rather than factoring them first.

Answer

There is no mistake because the limit still evaluates to $$\frac{3}{5}$$.

Answer

The error is in using polynomial long division instead of direct cancellation.

Limit of a Rational Function at Infinity

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