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