tiny-tim said:hi jmm12! welcome to pf!
tell us what you think (and why), and then we'll comment!
and that is NOT in general true. Since the denominator goes to 0, what must the numerator go to in order that this limit exist?
The first step in using limit laws to find the value of f(x) is to identify which limit law is applicable to the given function. Once you have determined the correct limit law, you can apply it to the function and evaluate the limit using algebraic manipulation and substitution.
There are several types of limit laws, including the sum law, difference law, product law, quotient law, and power law. Each of these laws has a specific purpose and can be used to simplify the evaluation of limits.
No, limit laws can only be applied to functions that are continuous at the point where the limit is being evaluated. If the function is not continuous, other methods, such as L'Hospital's rule, may need to be used to find the limit.
The squeeze theorem should be used when the limit of a function cannot be evaluated directly using limit laws. This may occur when the function is undefined at the point where the limit is being evaluated, or when the function is oscillating or discontinuous at that point.
Yes, there are some limitations to using limit laws. For example, limit laws cannot be used to evaluate limits at points where the function is undefined or at points of discontinuity. Additionally, some functions may require more advanced techniques, such as Taylor series, to find the limit.