Out-of-Bounds Calculus

Unexpected or surprising examples, interesting problems, and clever proofs on calculus that are often counterintuitive or paradoxical—the oddities that most math students are seldom exposed to during their calculus lessons.

Be it a continuous function whose graph possesses a tangent at no point, or a continuous function that has infinitely many maxima and minima on a finite interval, or a shape that has finite area but infinite perimeter, these examples of out-of-bounds calculus seldom fail to trigger an aha! reaction among math geeks.

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