[tex] \lim_{x \to \infty} 4 ^{x+1} - 1 / 4^x+3 =..... [/tex]

[tex]\displaystyle \lim_{x\to\infty}\frac{4^{x+1}-1}{4^x+3}=\lim_{x\to\infty}\frac{4^{x+1}-1}{4^x+3}\cdot\frac{\frac{1}{4^x}}{\frac{1}{4^x}}\\\lim_{x\to\infty}\frac{4^{x+1}-1}{4^x+3}=\lim_{x\to\infty}\frac{4-\frac{1}{4^x}}{1+\frac{3}{4^x}}\\\lim_{x\to\infty}\frac{4^{x+1}-1}{4^x+3}=\frac{4-\frac{1}{4^\infty}}{1+\frac{3}{4^\infty}}\\\lim_{x\to\infty}\frac{4^{x+1}-1}{4^x+3}=\frac{4-0}{1+0}\\\boxed{\boxed{\lim_{x\to\infty}\frac{4^{x+1}-1}{4^x+3}=4}}[/tex]