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lim[x→0] should not evaluate to ∞, it is undefined.
lim[x→0⁺] = ∞ lim[x→0⁻] = -∞
lim[x→0] should not evaluate to ∞, it is undefined.
lim[x→0⁺] = ∞
lim[x→0⁻] = -∞