For the following exercises determine the points if any at...

For the following exercises, determine the point(s), if any, at which each function is discontinuous. Classify any discontinuity as jump, removable, infinite, or other. a) f(x) = x / (x^2 - x) b) f(x) = (x + 3) / (x^2 + 5x + 6)

Transcript

00:01 So the first function is, so the first function is fx is equal to x upon x square, x upon x squared minus x.

00:14 So this is the first function.

00:16 So i can write this as x upon x into x minus 1.

00:21 The denominator should not be 0.

00:23 So out of domain, the function fx is not defined at x is equal to 0 and x is equal to 1.

00:31 The function is not defined at this point because we cannot make the domain to be 0.

00:38 Exact 0.

00:39 It can't be exact 0.

00:41 But so our point of consideration would be x is equal to 0 and x equal to 1.

00:47 First of all, let's check the left hand limit of, that is limit x tends to 1 minus limit x tends to 1 minus x upon x into x minus 1 minus x upon x into x minus 1 minus 1.

01:01 Which is equal to so it would be one upon one and one minus two just so this will this will be tending to this will be very zero but a negative zero so this will be tends to minus infinite and the right hand limit will be limit x tends to one plus so it would be x upon x into x minus one so it will tends to plus infinite so since left -hand limit is not equal to right hand limit, left hand limit is not equal to right hand limit.

01:39 Therefore limit does not exist.

01:41 Therefore limit at this point does not exist and it is discontinuous, discontinuous at x tends to 1 and the discontinuity is infinite discontinued...

Question

For the following exercises, determine the point(s), if any, at which each function is discontinuous. Classify any discontinuity as jump, removable, infinite, or other. a) f(x) = x / (x^2 - x) b) f(x) = (x + 3) / (x^2 + 5x + 6)

Please give Ace some feedback