Discuss the continuity of the function below at x=-3. Justify you work with limi

Anonym

Anonym

Answered question

2021-10-21

Discuss the continuity of the function below at x=-3. Justify you work with limits.
h(x)={x2+2x5x+7,x38,x=3

Answer & Explanation

2abehn

2abehn

Skilled2021-10-22Added 88 answers

Any function h(x) is continuous at x=a
if h(a)=h(a)=h(a+)
L.H.L=h(a)=R.H.L
We have:
h(x)={x2+2x5x+7,x38,x=3
h(3)=h(3,λ)=(3λ)2+2(3λ)53λ+7
9+λ2+6λ62λ54λ
λ2+4λ24λ
0+4×0240
24=12
h(3+)=h(3+λ)=(3+λ)2+2(3+λ)53+λ+7
=9+λ26λ6+2λ54+λ
=λ24λ24+λ
=024×024+0
=12
h(3)=8
Now we have
h(3)=h(3+)h(3)
Hence function h(x) is not continuous.

Jeffrey Jordon

Jeffrey Jordon

Expert2022-06-24Added 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?