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.

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

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

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

So answer is 2.