Întrebare Limite remarcabile

$$\lim_{x \to 3}\frac{2^{x}-8}{x-3}$$

As vrea sa stiu cum se rezolva pas cu pas.

Folosim formula:
$\underset{x\to a}{\mathop{\lim }}\,\frac{{{a}^{u(x)}}-1}{u(x)}=\ln a$ , $a>0,\underset{x\to a}{\mathop{\lim }}\,u(x)=0$

$\underset{x\to 3}{\mathop{\lim }}\,\frac{{{2}^{x}}-8}{x-3}=\underset{x\to 3}{\mathop{\lim }}\,\frac{8({{2}^{x-3}}-1)}{x-3} =8\cdot \underset{x\to 3}{\mathop{\lim }}\,\frac{{{2}^{x-3}}-1}{x-3}=8\ln 2=\ln {{2}^{8}}$ .

Faceți substituția t=x-3