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## Homework Statement

Explain in your own words what:

lim

*f(x)*= 5

x→2

means.

## Homework Equations

None

## The Attempt at a Solution

I wrote:

"As

*x*approaches 2, the limit of the function

*f(x)*is 5 (in other words,

*f(x)*approaches 5). The value of the function that is limited can be different than the limit of the function itself."

But I do not know if there can be a function value but with an undefined limit. I also want to say above that a function value may or may not be the same as the limit, and that either value may be undefined. But I don't know for sure if that is true.

For example, what is:

lim

*f(x)*if

*f(x)*=

*x*(in other words, if

*y*=

*x*)

x→1

Above we have a straight line graph with a slope of 1, and a y-intercept of 0.

But is the limit really 1? Even though the graph goes right through

*f(x)*= 1?