Question

Find all the values of x at which the function fails to be continuous.

Answer 1

Do you have a graphing calculator?

Answer 2

you want to find the values of x which make f(x) to not be a real number.

this usually implies that a root would be negative or that the denominator would be zero.

Answer 3

@Euler271 is there anyway of doing this problem without a graphing calculator? I'm not allowed to use them on test days

Answer 4

As @Euler271 said, we can't have a denominator of zero, since we can't divide by zero.

So set the denominator equal to zero, and solve for x:

1+sin(2x) = 0

Answer 5

@agent0smith is sin2x suppose to equal 2sinxcosx ?

Answer 6

Yes it is, but you don't need to use that identity here (and probably shouldn't, as it'll make it more difficult to solve).

Answer 7

oh ok ok.

Answer 8

@agent0smith These are my answer choices..how do I get to one of these? haha

Answer 9

1+sin(2x) = 0

First subtract 1 from both sides

sin(2x) = -1

now find where sin(angle) = -1. Use a unit circle if you need.

That will give you 2x = ...

Answer 10

0?

Answer 11

@agent0smith ?

Answer 12

sin0 = 1, not -1.

Answer 13

no wait.. 3pi/2 ?

Answer 14

Yes, but that's not your only solution... 3pi/2 + what? where is sine equal to -1 again?

Answer 15

I guess the only answer in the answer choices is \[2n \pi+\frac{ 3\pi }{ 2 }\] but I don't know how to get the 2npi

Answer 16

@agent0smith ?

Answer 17

Well remember you have \[\Large 2x = 2n \pi+\frac{ 3\pi }{ 2 }\]
so solve for x

Answer 18

npi +3pi/2

Answer 19

Not quite...

Answer 20

Try dividing both sides by 2 again, but make sure you do it right this time \[\Large 2x = 2n \pi+\frac{ 3\pi }{ 2 }\]

Answer 21

just kidding. sorry npi +3pi

Answer 22

Still not right

Answer 23

Half of it is, the other half isn't

Answer 24

aaaah is it just npi +3pi/2?

Answer 25

No.... divide both sides by 2. What is 3pi/2 divided by 2?

Answer 26

3pi

Answer 27

@agent0smith I thought I did put 3pi earlier :/

Answer 28

That's not correct.

Answer 29

\[\Large \frac{ \frac{ 3 \pi }{2 } }{2 } = \frac{ 3 \pi }{2 } *\frac{ 1 }{2 }\]

Answer 30

3pi/4 then.

Answer 31

I'm stoopid. sorry.

Answer 32

Better :)

Answer 33

haha it happens :P

Answer 34

so the answer is npi +3pi/4 ?

Answer 35

I just don't understand how you got the 2npi, though. before dividing by 2

Answer 36

Yep looks that way.

Answer 37

You got the 2npi...

Answer 38

It's because sine is equal to -1 at 3pi/2, and remember that sin(x+2pi) = sinx

Answer 39

If you keep going around the circle, it keeps repeating every 360 degrees.