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10 steps: (1) ε-δ definition of limit: lim(x→a)f(x)=L means for every ε>0, exists δ>0 such that 0<|x-a|<δ → |f(x)-L|<ε. (2) Proof example: prove lim(x→2)(3x-1)=5. Given ε, choose δ=ε/3. Then |3x-1-5|=|3x-6|=3|x-2|<3δ=ε. ✓ (3) CAUCHY SEQUENCES: {aₙ} is Cauchy if for every ε>0, exists N such that |aₘ-

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