So far we have worked with the idea of a limit and also
defined limits carefully using epsilon and delta. This page deals with
some properties of a limit under different conditions. The properties
that will be discussed here, assuming and , are:
The first property is saying when you take the limit of a sum, it is equal to the sum of the limits. The second one says when you multiply by a constant, L will also be multiplied by that constant. The third property says that the limit of a product is equal to the product of the limits. The last one says the limit of a quotient is equal to quotient of the limits.
Let's try to work some limit problems. Sometimes it may seem like the limit of a function is undefined since we are dividing by 0 in the denominator. If that happens we can work with the numerator to evaluate the limit. Take this limit for example:
Let's try one more problem that's a little bit more