Lim x-> x sin Х / 1 - Cos 2x

Lim x-> x sin Х / 1 – Cos 2x

DIKETAHUI

$sf limlimits_{x to0}dfrac{x :sin :x}{1 -cos :2x}$

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DITANYA

Nilai limitnya

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JAWAB

$sf limlimits_{x to0}dfrac{x :sin :x}{1 -cos :2x} = limlimits_{x to0}dfrac{x :sin :x}{1 -(1 -2sin^2:x)}$

$sf limlimits_{x to0}dfrac{x :sin :x}{1 -cos :2x} = limlimits_{x to0}dfrac{x :sin :x}{1 -1 +2sin^2:x}$

$sf limlimits_{x to0}dfrac{x :sin :x}{1 -cos :2x} = limlimits_{x to0}dfrac{x :sin :x}{2sin^2:x}$

$sf limlimits_{x to0}dfrac{x :sin :x}{1 -cos :2x} = dfrac{1}{2} limlimits_{x to0}dfrac{x : cancel{sin :x}}{sin:x : cancel{sin :x}}$

$sf limlimits_{x to0}dfrac{x :sin :x}{1 -cos :2x} = dfrac{1}{2} limlimits_{x to0}dfrac{x}{sin:x}$

$sf limlimits_{x to0}dfrac{x :sin :x}{1 -cos :2x} = dfrac{1}{2} times1$

$sf limlimits_{x to0}dfrac{x :sin :x}{1 -cos :2x} = dfrac{1}{2}$