1 3 properties of limits homework

First, we will use property 2 to break up the limit into three separate limits. We will then use property 1 to bring the constants out of the first two limits. Doing this gives us, We can now use properties 7 through 9 to actually compute the limit.

lim x→ac =c, c is any real number lim x → a c = c, c is any real number In other words, the limit of a constant is just the constant. You should be able to convince yourself of this by drawing the graph of f (x) =c f (x) = c.

This means that we can now do a large number of limits. This is a combination of several of the functions listed above and none of the restrictions are violated so all we need to do is plug in x = 3 x = 3 into the function to get the limit. Not a very pretty answer, but we can now do the limit.

We can now use properties 7 through 9 to actually compute the limit. In other words, in this case we see that the limit is the same value that we’d get by just evaluating the function at the point in question. This seems to violate one of the main concepts about limits that we’ve seen to this point.