Question

Let ModifyingBelow lim With x right arrow 6 f (x )equals 4 and ModifyingBelow lim With x right arrow 6 g (x )equals 6. Use the limit rules to find the following limit. ModifyingBelow lim With x right arrow 6 StartFraction f (x )plus g (x )Over 6 g (x )EndFraction

Answer 1

Answer:

5/3

Step-by-step explanation:

$\lim_{x \to 6} f(x) =4; and \lim_{x \to 6} g(x) =6\\ \lim_{x \to 6} \dfrac{f(x)+g(x)}{g(x)} =?$

Using the laws of limits,

$\\ \lim_{x \to 6} \dfrac{f(x)+g(x)}{g(x)} = \dfrac{lim_{x \to 6}f(x)+lim_{x \to 6}g(x)}{lim_{x \to 6}g(x)}, lim_{x \to 6}g(x)\neq 0$

Thus,

$\dfrac{lim_{x \to 6}f(x)+lim_{x \to 6}g(x)}{lim_{x \to 6}g(x)} =$$\frac{4+6}{6} =\frac{10}{6}=\frac{5}{3}$