[tex] \lim_{x \to \ 3} \frac{1 - cos (x - 3)}{x^{2} - 6x + 9 }[/tex] pliss pake cara lama gapapa a. 2 b. -2 c. 1/2 d -1/2 e. 1/3

[tex] \lim_{x \to \ 3} \frac{1 - cos (x - 3)}{x^{2} - 6x + 9 }\,\,\,\,\,\,\,\,[faktorkan\,\,sehingga][/tex]

[tex]= \lim_{x \to \ 3} \frac{1 - cos (x - 3)}{(x-3)^{2}}\,\,\,\,\,\,\,\,[ubah\,\,cos\,\,sesuai\,\,sifat\,\,trigonometri][/tex]

[tex]= \lim_{x \to \ 3} \frac{2\,sin^{2} (\frac{(x - 3)}{2})}{4( \frac{x-3}{2} )^{2}}\,\,\,\,\,\,\,\,[pisahkan][/tex]

[tex]= \frac{2}{4} \times \lim_{x \to \ 3} \frac{sin^{2} (\frac{(x - 3)}{2})}{( \frac{x-3}{2} )^{2}}\,\,\,\,\,\,\,\,[karena\,\,telah\,\,sesuai\,\,sifat\,\,trigonometri][/tex]

[tex]= \frac{2}{4} \times 1[/tex]

[tex]= \frac{2}{4}[/tex]

[tex]= \frac{1}{2}\,\,\,\,\,\,(c)[/tex]