Question

Tentukan hasil dari:
[tex]\displaystyle\lim_{x\to \pi} \frac{ {2x}^{2} - 6x\pi + {4\pi}^{2} }{ {x}^{2} - {\pi}^{2} } [/tex]
[tex] \\ [/tex]
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Answer 1

Verified answer

limit

bentuk 0/0

•

[tex]\displaystyle\lim_{x\to \pi} \frac{ {2x}^{2} - 6x\pi + {4\pi}^{2} }{ {x}^{2} - {\pi}^{2} } \\ \\ = \: \displaystyle\lim_{x\to \pi} \frac{ 2({x}^{2} - 3x\pi + {2\pi}^{2} )}{ {x}^{2} - {\pi}^{2} } \\ \\ = \: \displaystyle\lim_{x\to \pi} \frac{2(x - \pi)(x - 2\pi)}{(x - \pi)(x + \pi)} \\ \\ = \: \displaystyle\frac{2(\pi - 2\pi)}{\pi + \pi} \\ \\ = \: \displaystyle \: \frac{ - 2\pi}{2\pi} \\ \\ = \: \displaystyle - 1[/tex]