olymmath

HMMT 2009 K5

  • Calculus
  • Answer

Compute

lim⁡h→0sin⁡(π3+4h)−4sin⁡(π3+3h)+6sin⁡(π3+2h)−4sin⁡(π3+h)+sin⁡(π3)h4\lim _{h \rightarrow 0} \frac{\sin \left(\frac{\pi}{3}+4 h\right)-4 \sin \left(\frac{\pi}{3}+3 h\right)+6 \sin \left(\frac{\pi}{3}+2 h\right)-4 \sin \left(\frac{\pi}{3}+h\right)+\sin \left(\frac{\pi}{3}\right)}{h^{4}}

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{\sqrt{3}}{2}

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