Question

lim x-> 2 x^7-128/x^6-64 (trigonometry) no spam

Answer 1

$\sf{\underline{\underline{Question:}}}$


$\boxed{ \displaystyle \lim_{x \to 2} \frac{x^{7}-128}{x^{6}-64}}$


$\sf{\underline{\underline{Solution}}}$:


$= \displaystyle \lim_{x \to 2} \frac{x^{7}-128}{x^{6}-64}$


$= \displaystyle \lim_{x \to 2} \frac{x^{7}-2^{7}}{x^{6}-2^{6}}$


$= \displaystyle \lim_{x \to 2}$ $\frac{ \frac{ {x}^{7} - {2}^{7} }{x - 2} }{ \frac{ {x}^{6} - {2}^{6} }{x - 2} }$


$= \frac{\displaystyle \lim_{x \to 2} \frac{x^{7}-2^{7}}{x - 2}}{\displaystyle \lim_{x \to 2} \frac{x^{6}-2^{6}}{x - 2}}$


$= \frac{7 \times {2}^{6} }{6 \times {2}^{5} }$


$= \frac{7}{6} \times {2}^{6 - 5}$


$= \frac{7}{6} \times 2$


$=\boxed{ \frac{7}{3}}$


$\sf{\underline{Answer}}$: $\boxed{ \frac{7}{3}}$