Suppose f left parenthesis x right parenthesis right arrow 150f(x)→150 and g left parenthesis x right parenthesis right arrow 0g(x)→0 with g(x)less than< 0 as x right arrow 3x→3. determine modifyingbelow lim with x right arrow 3 startfraction f left parenthesis x right parenthesis over g left parenthesis x right parenthesis endfractionlimx→3 f(x) g(x).

Step-by-step explanation:

Given that:

f(x) approaches 150, and

g(x) approaches 0, with g(x) < 0,

as x approaches 3.

This means:

We need to evaluate:

Distributing the limit to numerator and denominator, we get:

The expression will result in infinity as the answer, but since, g(x) < 0, this means g(x) is approaching 0 from the negative side. As a result, the expression 150/0 will approach negative infinity as x will approach 3.

Therefore, we can conclude:

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!