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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

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  1. math456 Group Title
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    • one year ago
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    @cwrw238 @Hero

    • one year ago
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    @jim_thompson5910

    • one year ago
  4. jim_thompson5910 Group Title
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    what is cos(0)

    • one year ago
  5. math456 Group Title
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    its 1

    • one year ago
  6. jim_thompson5910 Group Title
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    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?

    • one year ago
  7. math456 Group Title
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    yea so that means \[\cos x \neq x=0\]

    • one year ago
  8. jim_thompson5910 Group Title
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    do you mean cos(x) doesn't equal x when x = 0?

    • one year ago
  9. math456 Group Title
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    yea because at x its 0 and at x<0 its 1

    • one year ago
  10. jim_thompson5910 Group Title
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    then you are correct, and this shows us that there is a discontinuity

    • one year ago
  11. math456 Group Title
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    alright kool thanks and does the graph looks like this?|dw:1348180882506:dw|

    • one year ago
  12. jim_thompson5910 Group Title
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    you're on the right track

    • one year ago
  13. jim_thompson5910 Group Title
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    however, you only graph cos(x) when x < 0

    • one year ago
  14. jim_thompson5910 Group Title
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    and you only graph 1 - x^2 when x > 0

    • one year ago
  15. jim_thompson5910 Group Title
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    make sure you draw a hole at (0,1) and a closed circle at (0,0)

    • one year ago
  16. math456 Group Title
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    |dw:1348181069990:dw| like this?

    • one year ago
  17. jim_thompson5910 Group Title
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    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

    • one year ago
  18. math456 Group Title
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    |dw:1348181225073:dw|

    • one year ago
  19. jim_thompson5910 Group Title
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    good, you got it

    • one year ago
  20. math456 Group Title
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    alright thanks for ur help!

    • one year ago
  21. jim_thompson5910 Group Title
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    np

    • one year ago
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