Angles in a Star

(A new question of the week) I like problems that can be solved in multiple ways, which can train us in seeing the world from different perspectives. Late in November we dealt with a pair of such questions involving angles in star-like figures.

Two Inside-Out Limit Problems

(A new question of the week) Limits can be challenging. They can be even more challenging when they require L’Hôpital’s rule or more advanced methods (Maclaurin series), and then are turned inside-out by asking not for the limit itself, but for parameters that will result in a specified limit, or what values of the limit …

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A Geometrical Limit

(A new question of the week) We usually see limits applied to functions in a calculus class. An interesting question from late October deals with a limit in a geometrical construction based on a function. We’ll be seeing how to discover a proof, then several alternative proofs, and finally what the answer means.

A Mind-Stretching Exercise with a Stretched Cosine

(A new question of the week) A question in September, about graphing a horizontally-stretched cosine function, led to a long conversation. Between a typo in the problem and some inside-out thinking, this surprisingly non-routine problem led to some good mind-stretching! I have edited this down considerably by removing distractions from the main ideas, but it …

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