## math456 Group Title Need help! Explain why the function is discontinuous at the given number a. Sketch the graph of the function! one year ago one year ago

1. math456 Group Title

2. math456 Group Title

@cwrw238 @Hero

3. math456 Group Title

@jim_thompson5910

4. jim_thompson5910 Group Title

what is cos(0)

5. math456 Group Title

its 1

6. jim_thompson5910 Group Title

so notice how in the first piece, the y value at x = 0 is 1 but the y value in the second piece at x = 0 is 0 Can you visualize what I'm describing?

7. math456 Group Title

yea so that means $\cos x \neq x=0$

8. jim_thompson5910 Group Title

do you mean cos(x) doesn't equal x when x = 0?

9. math456 Group Title

yea because at x its 0 and at x<0 its 1

10. jim_thompson5910 Group Title

then you are correct, and this shows us that there is a discontinuity

11. math456 Group Title

alright kool thanks and does the graph looks like this?|dw:1348180882506:dw|

12. jim_thompson5910 Group Title

you're on the right track

13. jim_thompson5910 Group Title

however, you only graph cos(x) when x < 0

14. jim_thompson5910 Group Title

and you only graph 1 - x^2 when x > 0

15. jim_thompson5910 Group Title

make sure you draw a hole at (0,1) and a closed circle at (0,0)

16. math456 Group Title

|dw:1348181069990:dw| like this?

17. jim_thompson5910 Group Title

closer, but now erase the piece of cos(x) that's to the right of x = 0 and erase the piece of 1 - x^2 that's to the left of x = 0

18. math456 Group Title

|dw:1348181225073:dw|

19. jim_thompson5910 Group Title

good, you got it

20. math456 Group Title

alright thanks for ur help!

21. jim_thompson5910 Group Title

np