Question

Use the given facts about the functions to find the indicated limit.

Answer 1

b. 2

Explanation:

Given that;

`\lim_(x \to -6) f(x)=2` and
`\lim_(x \to -6) g(x)=1`

Use the properties of limits;

`\lim_(x \to -6) ((f)/(g))(x)= \lim_(x \to -6) ((f(x))/(g(x)))`

`\lim_(x \to -6) ((f)/(g))(x)= ((\lim_(x \to -6)f(x))/(\lim_(x \to -6)g(x)))`

This implies that;

`\lim_(x \to -6) ((f)/(g))(x)= (2)/(1)`

`\lim_(x \to -6) ((f)/(g))(x)=2`

Answer 2

Answer: Option b.

Explanation:

1. You can rewrite it as following:

`\lim_(x\to \ -6) 2`

This means that you must substitute x=-6 into the limit. There is not x, then the function is always equal to 2, no matter the value of x.

`\lim_(x\to \ -6) 2=2`

`\lim_(x\to \ -6) 1`

This means that you must substitute x=-6 into the limit. There is not x, then the function is always equal to 1, no matter the value of x.

`\lim_(x\to \ -6) 1=1`

2. Then:

`\lim_(x\to \ -6) (f/g)(x)=2/1=2`

3. The answer 2.