Work through calculus and analysis problems with DeepSeek R1 with full rigor: justify limits and continuity, apply theorems only when their hypotheses hold, and verify derivatives and integrals by inverse operations.
## CONTEXT Calculus computations are easy to do quickly and wrong, and real analysis adds the requirement that every step be justified by a theorem whose hypotheses actually hold. DeepSeek R1 can compute derivatives and integrals fluently, but the failure modes are precisely the ones analysis was invented to prevent:…
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