When a limit approaches negative infinity, it means that the value of the function is becoming increasingly negative as the input approaches negative infinity. In other words, the function is decreasing without bound.
The natural logarithm function, ln(x), is undefined for negative inputs. Therefore, when we take the natural logarithm of (x^2-9), we are restricted to values of x that make the expression positive. As x approaches negative infinity, the expression (x^2-9) approaches positive infinity, allowing us to take the natural logarithm.
The result of taking the limit as x approaches negative infinity for ln(x^2-9) is negative infinity. This is because the function becomes increasingly negative as x approaches negative infinity, and the natural logarithm of a value approaching infinity is also infinity.
Yes, there is a restriction on the input for ln(x^2-9) when taking the limit as x approaches negative infinity. The expression (x^2-9) must be positive in order for us to take the natural logarithm. This means that x must be greater than -3 or less than 3.
To find the asymptotes of ln(x^2-9), we can set the limit as x approaches negative infinity equal to the vertical asymptote. In this case, the limit as x approaches negative infinity is equal to -∞, so the vertical asymptote is at x = -∞. This means that the graph of ln(x^2-9) approaches the vertical line x = -∞ as x decreases without bound.