Determine the left-hand limit of |x|/x as x approaches 0.

Unlock all questions

This demo includes only 20 questions. Upgrade to access hundreds of questions, flashcards, exam simulations, and disable ads.

Full question bankExam simulationsFlashcards
From $9.99Unlock all

Prepare for the DAY 2002A Limits Test with our targeted quiz. Test your understanding with flashcards and multiple-choice questions. Each question features hints and explanations to enhance your learning. Ace your exam!

Multiple Choice

Determine the left-hand limit of |x|/x as x approaches 0.

Explanation:
Think about the sign of x when you’re approaching 0 from the left. If x is negative, then |x| = -x. So |x|/x = (-x)/x = -1 for every x < 0. As x gets closer to 0 from the left, this value stays at -1, so the left-hand limit is -1. (From the right, it would be +1, since then |x| = x and |x|/x = 1, so the two one-sided limits differ.) The function isn’t defined at 0, which is why we talk about one-sided limits rather than a single limit.

Think about the sign of x when you’re approaching 0 from the left. If x is negative, then |x| = -x. So |x|/x = (-x)/x = -1 for every x < 0. As x gets closer to 0 from the left, this value stays at -1, so the left-hand limit is -1. (From the right, it would be +1, since then |x| = x and |x|/x = 1, so the two one-sided limits differ.) The function isn’t defined at 0, which is why we talk about one-sided limits rather than a single limit.

More Multiple Choice Questions
Subscribe

Get the latest from Examzify

You can unsubscribe at any time. Read our privacy policy