Evaluate lim_{x→0} x^2 / |x|.

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Prepare for the DAY 2002A Limits Test with interactive quizzes, detailed explanations, and various study resources. Strengthen your understanding of limits concepts and ace your exam!

Multiple Choice

Evaluate lim_{x→0} x^2 / |x|.

Explanation:
As x approaches zero, look at x^2/|x|. For any nonzero x, x^2 = (|x|)^2, so x^2/|x| = (|x|)^2/|x| = |x|. Thus near zero the expression behaves like |x|, which goes to 0 from both sides as x→0. Therefore the limit exists and equals 0.

As x approaches zero, look at x^2/|x|. For any nonzero x, x^2 = (|x|)^2, so x^2/|x| = (|x|)^2/|x| = |x|. Thus near zero the expression behaves like |x|, which goes to 0 from both sides as x→0. Therefore the limit exists and equals 0.

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