Write out each step of the 3-step test for continuity for the following functions at the given point. if the function is discontinuous, state the type of discontinuity

If we simply substitute the value x=2 in the expression we have

which is undefined.

But if we factor both numerator and denominator, we have

Since we are studying the limit as x approaches 2, we can assume that x is not 2. In this case, we can simplify the (x-2) parenthesis, and the expression becomes

And we can evaluate this at 2 with no problems:

So, we have

This means that in this case both left and right limits exist and are the same, so the limit exists, but the function is not defined at x=2. This is a removable discontinuity, because we can define the function as its limit, and we have a continuous function at x=2:

i got 10.28 but that rounds up to 10.3

ratio is 2 : 9

the answer is three

13.5 : 3