8 details my notes ask your teacher determine the set of...

Name: 8 details my notes ask your teacher determine the set of points at which the function is continuous fx y cossqrt1 x y x yy ge x x yy x x yy ge x 1 x yy le x 1 x yy x 1 18366
Uploaded: 2021-08-26T00:18:11-08:00
Duration: 4 min 9 s
Channel: Linda Hand
Description: 8 details my notes ask your teacher determine the set of points at which the function is continuous fx y cossqrt1 x y x yy ge x x yy x x yy ge x 1 x yy le x 1 x yy x 1 18366

8. DETAILS MY NOTES ASK YOUR TEACHER Determine the set of points at which the function is continuous. $F(x, y) = \cos(\sqrt{1 + x - y})$ $\{(x, y)|y \ge x\}$ $\{(x, y)|y > -x\}$ $\{(x, y)|y \ge x - 1\}$ $\{(x, y)|y \le x + 1\}$ $\{(x, y)|y > x + 1\}$

Transcript

00:01 Okay, we have three functions going on here.

00:04 We have the cosine of something.

00:07 We have the square root of something, and then we have one plus x minus y.

00:12 Okay, the cosine function is continuous everywhere.

00:19 So on minus infinity to infinity.

00:21 Okay, and you know that because here's what the cosine looks like.

00:26 There ain't no holes or anything in it.

00:29 Okay, the square root function is continuous everywhere on its domain.

00:34 Okay so remember the square root if you just have for example f of x equals the square root of x it's only defined for x greater than or equal to zero so this square root here is only defined when the underneath stuff is positive or zero because you can't take the square root of a negative number okay so i'm gonna say square root is continuous everywhere on its domain okay, so you could say that about the cosine too, but its domain is minus infinity to infinity.

01:16 Okay, so square root is continuous everywhere on its domain means we have some work to do on that part.

01:23 And then 1 plus x minus y, that's continuous everywhere.

01:28 1 plus x minus y continuous everywhere.

01:32 Oops, because x is continuous, y is continuous, adding, subtracting continuous.

01:44 All right, so now we have to work on.

01:46 The middle part here what we have to do is make sure one plus x minus y is greater than or equal to zero so minus y greater than or equal to minus x plus one oops minus one or y is less than or equal to x plus one all right x plus one that is a line starts at one has slope one okay so it's either the area on the top or the bottom of that line so just pick a point to plug in and see what happens.

02:33 I'm going to pick zero zero.

02:35 If i plug that in and i get zero is less than zero plus one...

Question

8. DETAILS MY NOTES ASK YOUR TEACHER Determine the set of points at which the function is continuous. $F(x, y) = \cos(\sqrt{1 + x - y})$ $\{(x, y)|y \ge x\}$ $\{(x, y)|y > -x\}$ $\{(x, y)|y \ge x - 1\}$ $\{(x, y)|y \le x + 1\}$ $\{(x, y)|y > x + 1\}$

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