Limits Question

Question

i) Using the graph of the function f, evaluate the limit of f(x) as x approaches 1⁺.

ii) Using the graph of the function f, evaluate the limit of f(x) as x approaches 2.

Answer 1

Hi Shade.

Part i)

This question asks us for the limit as x approaches 1⁺ which is just a notation for saying "From the right-hand side". To solve for this, follow the graph, starting from the right and moving leftwards until you reach the x value of 1.

Here you see that the graph slowly approaches 2 since we started from the right side of the graph. While the value at x = 1 may not be 2, we are looking for the limit, not the value. Therefore...

The limit as x approaches 1⁺ is 2

Part ii)

Now for the second part, it asks for the limit as x approaches 2, and for this, you can simply look at the graph and notice that if we start from the left and work rightwards or start from the right and work leftwards, the graph approaches the same value as we get closer to x = 2.

That being said, the limit as x approaches 2 is 1 (the y value at x = 2)