Analtical method to evaluate
Lim
X -> -infinite
To evaluate the limit when x approaches negative infinity, you can follow these steps using an analytical method:
1. Determine the expression inside the limit. Let's call it f(x).
2. Examine the highest power of x in the denominator and the numerator of f(x). If the denominator has a higher power of x, the limit will approach zero. If the numerator has a higher power of x, the limit will either be positive or negative infinity, depending on the sign of the highest power.
3. Analyze the coefficients of the highest power term. If the coefficients in the numerator and denominator are different, the limit will approach either positive or negative infinity, depending on the signs of the coefficients. If the coefficients are the same, the limit will approach a finite value.
4. After considering steps 2 and 3, simplify the expression by dividing both the numerator and denominator by the highest power of x. This will help identify the limiting behavior.
5. If there are still undetermined terms (e.g., an indeterminate form like 0/0 or ∞/∞), you can apply further techniques such as L'Hôpital's rule or factoring to simplify the expression and determine the limit.
Applying these steps will help you evaluate the limit as x approaches negative infinity using an analytical method. Remember to carefully analyze the exponents and coefficients in order to determine the limiting behavior of the expression.