Question

Determine whether the limit exists or not

Answer 1

B

Explanation:

The limit of quotient of two functions is the quotient of their limits, provided that the limit in the denominator function is not zero:

`\lim_(x\to x_0)(g(x))/(h(x))=( \lim_(x \to x_0) g(x) )/( \lim_(x \to x_0) h(x) ), \text{ where }\lim_(x \to x_0) h(x)\\eq 0.`

In your case,

`\lim_(x \to 4) h(x)=-2\\eq 0,`

then

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