The rigorous study of limits.
Prove that
lim (3x - 7) = 5.
x→4
0 < x - 4 < δ → 3x - 7 - 5 < ε
3x - 12 < ε
3 (x - 4) < ε
x - 4 < ε/3
δ = ε/33x - 12 < δ
3 (x - 4) < 3δ = εD E M O S T R A D O
Prove that
lim (3x - 7) = 5.
x→4
0 < x - 4 < δ → 3x - 7 - 5 < ε
3x - 12 < ε
3 (x - 4) < ε
x - 4 < ε/3
δ = ε/33x - 12 < δ
3 (x - 4) < 3δ = εD E M O S T R A D O
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