Question

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.)

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:

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