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Day 175 — 365 Problems for 365 Days AP Calculus limit with square roots and cancellation: lim x->0 ( sqrt(1 x) - 1 - (1/2)x ) / x^2 This is a classic “designed cancellation” limit. The expression sqrt(1 x) starts with 1 (1/2)x, so subtracting 1 and (1/2)x removes the first two terms and forces you to find the first nonzero term. You can solve it with a short Taylor/binomial expansion, or by rationalizing carefully and simplifying to a clean constant. Project Mentor helps high school students wit
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🔥 Day 146 — 2026 MIT Integration Bee (Qualifying) Q12 Evaluate: Integral from 0 to 1 of sqrt(x^2 x sqrt(x^2 x sqrt(x^2 x …))) dx This is an “infinite nested radical” problem that looks impossible… until you use self-similarity. Let the whole radical be y. Then the inside contains y again, which gives you a clean equation to solve before you integrate. Hints: \t•\tLet y = sqrt(x^2 x sqrt(x^2 x …)) \t•\tThen y = sqrt(x^2 x y) \t•\tSolve for y on [0, 1], then integrate 📣 Project Mentor: free guid
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