Penjelasan dengan langkah-langkah:
[tex] = \lim \limits_{x \to\pi} \frac{1 + \cos(x) }{x - \pi} [/tex]
[tex] = \lim \limits_{x \to\pi} \frac{1 + \cos(x) }{x - \pi} \times \frac{1 - \cos(x) }{1 - \cos(x) } [/tex]
[tex] = \lim \limits_{x \to\pi} \frac{1 - \cos {}^{2} (x) }{(x - \pi)(1 - \cos(x)) } [/tex]
[tex] = \lim \limits_{x \to\pi} \frac{ \sin {}^{2} (x) }{(x - \pi)(1 - \cos(x)) } [/tex]
[tex] = \lim \limits_{x \to\pi} \frac{ \sin {}^{2} (\pi - x) }{(x - \pi)(1 - \cos(x)) } [/tex]
[tex] = \lim \limits_{x \to\pi} \frac{ \sin {}^{2} ( - 1.( x - \pi)) }{(x - \pi)(1 - \cos(x)) } [/tex]
[tex] = \lim \limits_{x \to\pi} \frac{ \sin( - 1.(x - \pi)) }{x - \pi} \times \lim \limits_{x \to\pi} \frac{ \sin( - 1.(x - \pi) )}{1 - \cos(x) } [/tex]
[tex] = \lim \limits_{u \to0} \frac{ \sin( - 1.u) }{u} \times \lim \limits_{x \to\pi} \frac{ \sin( - 1.(\pi - x)) }{1 - \cos(x) } [/tex]
[tex] = \frac{ - 1}{1} \times \frac{ \sin( - 1.(\pi - \pi) )}{1 - \cos(\pi) } [/tex]
[tex] = - 1 \times \frac{ \sin( - 1.0) }{ 1 - ( - 1)} [/tex]
[tex] = - 1 \times \frac{ \sin(0) }{2} [/tex]
[tex] = - 1 \times \frac{0}{2} [/tex]
[tex] = 0[/tex]
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