Answer
The values of f(x) get closer and closer to the number "L" as the values of x gets closer and closer to "a".
We try values of x closer and closer to "5" and find that the limit is "1".
Work Step by Step
The definition of the limit of a function f(x) on page 898 of the textbook on page 898 directly answers the first part of our question.
The second part of the question is asks us to find the limit as x approaches 5 of $\frac{x-5}{x-5}$. We do this by trying values that are getting closer and closer to 5, without actually plugging in 5.
Two decimal numbers close to 5 are 4.9 and 5.01.
Now if we plug in 4.9, 4.99, 4.999, etc. and 5.01, 5.001, 5.0001 etc. we are trying numbers that are approaching 5.
When we plug all these numbers in, it is easy to see that the limit is 1.
