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Find all values x = a where the function is discontinuous. For each value of x, give the limit of the function as x approaches a. Be sure to note when the limit doesn't exist. f(x) = 8 + x / x(x - 2) Select the choice below and, if necessary, fill in the answer box(es) within your choice. (Use a comma to separate answers as needed.) A. The function f is discontinuous over the interval 0. The limit is 2. (Type your answer in interval notation.) B. The function f is discontinuous at the two values x = . The limit for the smaller value is . The limit for the larger value is . C. The function f is discontinuous at the two values x = . The limit for the smaller value does not exist and is not ? or -?. The limit for the larger value is . D. The function f is discontinuous at the single value x = . The limit does not exist and is not ? or -?. E. The function f is discontinuous over the interval . The limit does not exist and is not ? or -?. (Type your answer in interval notation.) Click to select and enter your answer(s) and then click Check Answer.

          Find all values x = a where the function is discontinuous. For each value of x, give the limit of the function as x approaches a. Be sure to note when the limit doesn't exist.

f(x) = 8 + x / x(x - 2)

Select the choice below and, if necessary, fill in the answer box(es) within your choice.
(Use a comma to separate answers as needed.)

A. The function f is discontinuous over the interval 0. The limit is 2.
(Type your answer in interval notation.)
B. The function f is discontinuous at the two values x = . The limit for the smaller value is . The limit for the larger value is .
C. The function f is discontinuous at the two values x = . The limit for the smaller value does not exist and is not ? or -?. The limit for the larger value is .
D. The function f is discontinuous at the single value x = . The limit does not exist and is not ? or -?.
E. The function f is discontinuous over the interval . The limit does not exist and is not ? or -?.
(Type your answer in interval notation.)

Click to select and enter your answer(s) and then click Check Answer.

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Find all values x = a where the function is discontinuous. For each value of x, give the limit of the function as x approaches a. Be sure to note when the limit doesn't exist.

f(x) = 8 + x / x(x - 2)

Select the choice below and, if necessary, fill in the answer box(es) within your choice.
(Use a comma to separate answers as needed.)

A. The function f is discontinuous over the interval 0. The limit is 2.
(Type your answer in interval notation.)
B. The function f is discontinuous at the two values x = . The limit for the smaller value is . The limit for the larger value is .
C. The function f is discontinuous at the two values x = . The limit for the smaller value does not exist and is not ? or -?. The limit for the larger value is .
D. The function f is discontinuous at the single value x = . The limit does not exist and is not ? or -?.
E. The function f is discontinuous over the interval . The limit does not exist and is not ? or -?.
(Type your answer in interval notation.)

Click to select and enter your answer(s) and then click Check Answer.

Added by Angela B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Andrew Noble

09/16/2022

Step 1

Given function f(x) = (8 + x) / (x(x - 2)), the function is discontinuous at x = 0 and x = 2 because the denominator becomes 0 at these points. Show more…

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Find all values x = a where the function is discontinuous. For each value of x, give the limit of the function as x approaches a. Be sure to note when the limit doesn't exist. f(x) = 8 + x / x(x - 2) Select the choice below and, if necessary, fill in the answer box(es) within your choice. (Use a comma to separate answers as needed.) A. The function f is discontinuous over the interval. The limit is. (Type your answer in interval notation.) B. The function f is discontinuous at the two values x = . The limit for the smaller value is . The limit for the larger value is . C. The function f is discontinuous at the two values x = . The limit for the smaller value does not exist and is not ∞ or -∞. The limit for the larger value is . D. The function f is discontinuous at the single value x = . The limit does not exist and is not ∞ or -∞. E. The function f is discontinuous over the interval . The limit does not exist and is not ∞ or -∞. (Type your answer in interval notation.) Click to select and enter your answer(s) and then click Check Answer.

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Transcript

00:01 Here we're given a function f of x, which is equal to 8 plus x divided by x times x minus 2.

00:10 And we're asked to find where is this continuous, discontinuous.

00:15 And then for each of those values, we want to find the limit as x approaches that value.

00:20 So let's start off by finding where is it discontinuous.

00:24 Well, it's going to be discontinuous anywhere the denominator is equal to zero.

00:28 So i'm going to get x is one of the factors.

00:31 So x equals 0 is one of the factors because i set that factor equal to 0.

00:37 I'm going to have another one because if x minus 2 is 0, the denominator is 0 as well.

00:42 So if i add 2, i'm going to get that x is equal to 2.

00:46 So i have two values that are discontinuous.

00:49 Now let's find the limit as x approaches each of those values.

00:52 So the limit as x approaches 0 of f of x.

00:57 Well, if i just blindly plug it in, i'm going to get 8 divided by 0.

01:02 That tells me the answer has to be infinite, but it doesn't tell me if it exists or not, because it could be plus or minus or both.

01:10 So now let's take a look at the left side and the right side.

01:15 So if i were to say, you know what, x is approaching zero, but x is always going to be a slightly negative number...

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