Answer:
[tex]\lim_{x \to \infty} \frac{x+6}{x+7}[/tex] = 1
Step-by-step explanation:
You have to calculate the following limit:
[tex]\lim_{x \to \infty} \frac{x+6}{x+7}[/tex]
To solve the previous limit, you can factor x from numerator and denominator of the function, and use the fact that c/∞ = 0 with c a constant.
[tex]\lim_{x \to \infty} \frac{x+6}{x+7}= \lim_{x \to \infty}\frac{x(1+\frac{6}{x})}{x(1+\frac{7}{x})}=\lim_{x \to \infty}\frac{1+6/x}{1+7/x}=\frac{1+0}{1+0}=1[/tex]
Hence, the limit is 1, L = 1
