Nilai lim_(x→0)⁡ (cos⁡(x+a)-cos⁡(x-a))/x=⋯

Bahas Soal Matematika » Limit ›

Nilai $\displaystyle \lim_{x\to 0} \ \frac{\cos (x+a) - \cos (x-a)}{x} = \cdots$

Pembahasan:

$\begin{aligned} \lim_{x\to 0} \ \frac{\cos (x+a) - \cos (x-a)}{x} &= \lim_{x\to 0} \ \frac{-2 \sin \frac{1}{2} ((x+a)+(x-a)) \sin \frac{1}{2} ((x+a)-(x-a))}{x} \\[8pt] &= \lim_{x\to 0} \ \frac{-2 \sin x \ \sin a}{x} \\[8pt] &= -2 \sin a \ \cdot \ \lim_{x\to 0} \ \frac{\sin x}{x} \\[8pt] &= -2 \sin a \ \cdot \ 1 \\[8pt] &= -2 \sin a \end{aligned}$

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Bahas Soal Matematika » Limit ›

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Bahas Soal Matematika » Limit ›