Soal Limit Fungsi [tex] \lim_{x \to \ 2} \frac{ x^{n} - 2^{n} }{x-2} = 80[/tex] Tentukan nilai n!

smoga jwabannya dpat mmbantu

[tex] \frac{ {x}^{n} - {2}^{n} }{x - 2} = 80 \\ = \frac{nx {}^{n - 1} - {2n}^{n - 1} }{1} = 80 \\ = (n - 1) {nx}^{n - 2} - (n - 1) {2n}^{n - 2} = 80 \\ = {n}^{2} - n {(2)}^{n - 2} - 2n + {2n}^{n - 2} = 80 \\ = {n}^{2} - 2n = 80 \\ n(n - 2) = 80 \\ n = 10[/tex]
Semoga bermanfaat.....
-Prisco