find the limit of f(x) = \\frac{12}{x}-3 as x approaches ∞ and as x approaches -∞. lim f(x) = -3 x→∞ (type a…

find the limit of f(x) = \\frac{12}{x}-3 as x approaches ∞ and as x approaches -∞. lim f(x) = -3 x→∞ (type a simplified fraction.) lim f(x) = x→ -∞ (type a simplified fraction.)

find the limit of f(x) = \\frac{12}{x}-3 as x approaches ∞ and as x approaches -∞. lim f(x) = -3 x→∞ (type a simplified fraction.) lim f(x) = x→ -∞ (type a simplified fraction.)

Answer

Explanation:

Step1: Analyze limit as x approaches infinity

As (x\to\infty), the term (\frac{12}{x}\to0) because the denominator is getting infinitely large. So (f(x)=\frac{12}{x}-3\to0 - 3=- 3).

Step2: Analyze limit as x approaches negative - infinity

As (x\to-\infty), the term (\frac{12}{x}\to0) since the magnitude of the denominator is getting infinitely large. Then (f(x)=\frac{12}{x}-3\to0 - 3=-3).

Answer:

(\lim_{x\to-\infty}f(x)= - 3)