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This Curve Looks Simple At First, But It Gets Complicated Quickly

Calculus Level 3

Consider the above curve as the number of steps tends to infinity. Which of the following is true:

The curve goes through every point in the unit square The curve does not go through the point \( (\frac{1}{2},\frac{1}{2}) \) The curve does not go through the point \( (\frac{\sqrt{2}}{2}, \frac{\sqrt{3}}{3}) \) The curve does not go through the point \( ( \frac{1}{3},\frac{2}{3}) \)

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

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including olympiad champions, researchers, and professionals.

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View solutions

by Chung Gene Keun

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