Describe the interval on which the function is continuous.f(x)=\begin{ca

Emily-Jane Bray

Emily-Jane Bray

Answered question

2021-10-29

Describe the interval on which the function is continuous.
f(x)={x264x8,x816,x=8

Answer & Explanation

liingliing8

liingliing8

Skilled2021-10-30Added 95 answers

Consider the function
f(x)={x264x8,x816,x=8
Check the continuity of the function at x=8.
The left hand limit of the function at x=8 is given by
limx8f(x)=limx8(x264x8)
=limx8(x282x8)
=limx8((x8)(x+8)x8)
=limx8(x+8)
=8+8
=16
And the right hand limit at x=8 is
limx8+f(x)=limx8+(x264x8)
=limx8+(x282x8
=limx8+((x8)(x+8)x8)
=limx8+(x+8)
=8+8
=16
Also the function value at x=8 is 16.
Since the left hand limit and right hand limits are equal to the function value at x=8. so the limit exist and function is continuous at x=8.
Thus, the given function is continuous everywhere, or in interval notation, function is continuous on the interval (,).

Jeffrey Jordon

Jeffrey Jordon

Expert2022-08-30Added 2605 answers

Answer is given below (on video)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?