Left and right limits of piecewise function at x=2

[nycmathguy]

Homework Statement

Graphs & Functions

Relevant Equations

Piecewise Functions

Use the graph to investigate

(a) lim of f(x) as x→2 from the left side.

(b) lim of f(x) as x→2 from the right side.

(c) lim of f(x) as x→2.

Question 20

For part (a), as I travel along on the x-axis coming from the left, the graph reaches a height of 4. The limit is 4. It does not matter if there is a hole at (2, 4), right?

For part (b), as I travel along on the x-axis coming from the right, the graph reaches a height of 2. The limit is 2. It does not matter if there is a hole at (2, 2), right?

For part (c), LHL DOES NOT EQUAL RHL.

I conclude the limit does not exist.

You say?

 

[Mark44]

Yes to all.

 

[nycmathguy]

Yes to all.

I got another question right. It's a miracle. I need to understand this limit idea better. I know that limits in calculus 3 are more involved.