← Calculus

How to solve

The fundamental limit sin(u)/u → 1 scales: sin(kx)/x → k, and (1 − cos x)/x → 0.

Steps

  1. Rewrite to expose sin(kx)/(kx).
  2. Each sin(kx)/(kx) factor tends to 1.
  3. Multiply the leftover constants.

Example

lim x→0 sin(5x)/x

  1. sin(5x)/x = 5 · sin(5x)/(5x).
  2. → 5 · 1 = 5.

Answer: 5

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