Question

limf(x) = 3 and lime(x) = -620. Given thatEvaluate the followinglim [f(x) * g(x)]g(x)-f(x)[A] -2[B] 5[C]2[D] -6ABO O O O

Answer 1

Determine the value of expression by using the properties of the limit.

`\begin{gathered} \lim _(x\to c)(\lbrack f(x)\cdot g(x)\rbrack)/(g(x)-f(x))=(\lim _(x\to c)\lbrack f(x)\cdot g(x)\rbrack)/(\lim _(x\to c)\lbrack g(x)-f(x)\rbrack) \\ =(\lim _(x\to c)f(x)\cdot\lim _(x\to c)g(x))/(\lim _(x\to c)g(x)-\lim _(x\to c)f(x)) \end{gathered}`

Subtitute the given values of the function for the given in the given expression.

`\begin{gathered} (\lim _(x\to c)f(x)\cdot\lim _(x\to c)g(x))/(\lim _(x\to c)g(x)-\lim _(x\to c)f(x))=(3\cdot(-6))/(-6-3) \\ =(-18)/(-9) \\ =2 \end{gathered}`

So answer is 2.