Question

Find the limit (Picture Provided)

Answer 1

As long as
`g(x)` (or whichever function appears in the denominator) does not approach 0 as
`x\to c`,

`\displaystyle\lim_(x\to c)(f(x))/(g(x))=(\lim\limits_(x\to c)f(x))/(\lim\limits_(x\to c)g(x))`

In this case,

`\displaystyle\lim_(x\to4)\frac gh(x)=\lim_(x\to4)(g(x))/(h(x))=\frac0{-2}=2`

so the answer is B.

Answer 2

b. 0

Step-by-step explanation

We use the property of limits;

`lim_(x\to 4) (g)/(h) (x) = lim_(x\to 4) (g(x))/(h(x))`

`lim_(x\to 4) (g)/(h) (x) = (lim_(x\to 4)g(x))/(lim_(x\to 4)h(x))`

Substitute,

`lim_(x\to 4) (g)/(h) (x) = (0)/( - 2)`

Simplify;

`lim_(x\to 4) (g)/(h) (x) =0`