Continuity

[agl89]

Is f(x) = (x + 2) / (x^2 - 4) continuous at x = 1?

(1 + 2) / (1^2 - 4) = -1
∴ f(x) is continuous at x = 1


Is this correct?


Also...

Is f(x) = (x + 2) / (x^2 - 4) continuous at x = -2?

(-2 + 2) / (-2^2 - 4) = DNE

(x + 2) / (x^2 - 4)
= (x + 2) / [(x + 2)(x - 2)]
= 1 / (x - 2)

1 / ((-2) - 2)
= -1/4
∴ f(x) has a removable discontinuity at x = -2

 

[pka]

Is f(x) = (x + 2) / (x^2 - 4) continuous at x = 1?
(1 + 2) / (1^2 - 4) = -1
∴ f(x) is continuous at x = 1
Also...
Is f(x) = (x + 2) / (x^2 - 4) continuous at x = -2?
(-2 + 2) / (-2^2 - 4) = DNE
(x + 2) / (x^2 - 4)
= (x + 2) / [(x + 2)(x - 2)]
= 1 / (x - 2)
1 / ((-2) - 2)
= -1/4 ∴ f(x) has a removable discontinuity at x = -2

Yes those are correct.

 

[agl89]

Yes those are correct.

Thank you.