Compute lim(x→0) (e^(3x) - 1)/x

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TextLimits of Polynomial Functions

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Find the limits: (i) lim[x→1] [x³ - x² + 1] (ii) lim[x→3] [x(x+1)] (iii) lim[x→-1] [1 + x + x² + ... + x¹⁰]

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Let a₁, a₂, . . ., aₙ be fixed real numbers and define a function f(x) = (x - a₁)(x - a₂)...(x - aₙ). What is lim[x→a₁] f(x)? For some a ≠ a₁, a₂, ..., aₙ, compute lim[x→a] f(x).

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Evaluate lim(x→1) log_e(x)/(x - 1)

TextLimits of Polynomial Functions