Taylor Series Explorer

CSC-212 · Semester III · Numerical Methods

Taylor polynomial of e^{kx}

Guided practice — solve each problem, check, then generate a fresh one.

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Formula to apply

e^{kx} ≈ 1 + kx + (kx)²/2 + (kx)³/6

Problem

Compute the degree-3 Taylor polynomial of e^{3x} at x = 1.

Working

  1. 1T₃(x) = 1 + 3x + (3x)²/2 + (3x)³/6.
  2. 2At x = 1: kx = 3.
  3. 3T₃ = 1 + 3 + 4.5 + 4.5 = 13.