Question

Explain why the function is discontinuous at the given number a. (Select all that apply.) f(x) = { (x^2 - 5x) / (x^2 - 25) if x ? 5 1 if x = 5 a = 5 f(5) is defined and lim_{x ? 5} f(x) is finite, but they are not equal. lim_{x ? 5} f(x) does not exist. f(5) is undefined. lim_{x ? 5^+} f(x) and lim_{x ? 5^-} f(x) are finite, but are not equal. none of the above Sketch the graph of the function.

          Explain why the function is discontinuous at the given number a. (Select all that apply.)
f(x) = {
(x^2 - 5x) / (x^2 - 25) if x ? 5
1 if x = 5
a = 5
f(5) is defined and lim_{x ? 5} f(x) is finite, but they are not equal.
lim_{x ? 5} f(x) does not exist.
f(5) is undefined.
lim_{x ? 5^+} f(x) and lim_{x ? 5^-} f(x) are finite, but are not equal.
none of the above
Sketch the graph of the function.

Explain why the function is discontinuous at the given number a. (Select all that apply.)
f(x) =
(x^2 - 5x) / (x^2 - 25) if x ? 5
1 if x = 5
a = 5
f(5) is defined and limx ? 5 f(x) is finite, but they are not equal.
limx ? 5 f(x) does not exist.
f(5) is undefined.
limx ? 5^+ f(x) and limx ? 5^- f(x) are finite, but are not equal.
none of the above
Sketch the graph of the function.

Added by Rebecca A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Ben Blakesley

02/06/2022

Step 1

The function is defined as x^2 for all values of x except when x = 5. This means that the function is not defined at x = 5, which makes it discontinuous at that point. Show more…

Show all steps

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Explain why the function is discontinuous at the given number a. (Select all that apply.) f(x) = { (x^2 - 5x)/(x^2 - 25) if x != 5, 1 if x = 5 a = 5 f(5) is defined and lim_{x->5} f(x) is finite, but they are not equal. lim_{x->5} f(x) does not exist. f(5) is undefined. lim_{x->5^+} f(x) and lim_{x->5^-} f(x) are finite, but are not equal. none of the above Sketch the graph of the function.