Activity 5.1.2.
Complete the following table by entering “\(\infty\text{,}\)”“\(-\infty\text{,}\)”“\(0\text{,}\)” or “no limit” to identify how the function behaves as either \(x\) increases or decreases without bound. As much as possible, work to decide the behavior without using a graphing utility.
| \(f(x)\) | \(\lim_{x \to \infty} f(x)\) | \(\lim_{x \to -\infty} f(x)\) |
| \(e^x\) | ||
| \(e^{-x}\) | ||
| \(\ln(x)\) | ||
| \(x\) | ||
| \(x^2\) | ||
| \(x^3\) | ||
| \(x^4\) | ||
| \(\frac{1}{x}\) | ||
| \(\frac{1}{x^2}\) | ||
| \(\sin(x)\) |
