Question

evaluate lim x-> π/3
$\frac{sqrt{1 - \cos(6x)} }{ \sqrt{2}( \frac{\pi}{3} - x)}$

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Answer 1

Answer:

Let x=y+π/3

limx→π/3(1−cos6x)1/22–√(π3−x)=limy→0(1−cos6y)1/2−2–√y

then use standard limit

1−cosxx2→12

and observe that

y>0⟹y=y2−−√

y<0⟹y=−