Question

Select the correct answer.

Which type of discontinuity exists at x = 2 for f(x)=x^2-4/x-2?


A.

removable discontinuity


B.

jump discontinuity


C.

infinite discontinuity


D.

none of the above

Answer 1

Answer: The above answer is correct.

A. removable discontinuity

Step-by-step explanation: I got this right on Edmentum

Answer 2

Answer A.

Explanation:

Recall that
`f(x) = (x^2-4)/(x-2)`

we will calculate the lateral limits of f when x approches x=2. Note that

`\lim_(x\to 2^(+)) (x^2-4)/(x-2) = \lim_(x\to 2^(+)) ((x-2)(x+2))/(x-2) = 2+2 = 4`

`\lim_(x\to 2^(-)) (x^2-4)/(x-2) = \lim_(x\to 2^(-)) ((x-2)(x+2))/(x-2) = 2+2 = 4`

We can clasify the discontinuity as follows:

- Removable discontinuity if both lateral limits are equal and finite.

- Jump discontinuity if both lateral limits are finite but different.

- Essential discontinuity if one of the limits is not finite and the other one is finite.

Based on this classification, since both lateral limits are equal, the discontinuity is a removable discontinuity