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tmagloire1

  • one year ago

http://prntscr.com/88wnz4 ap calc ab

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  1. jim_thompson5910
    • one year ago
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    So you need your answer checked? Or you also need an explanation?

  2. tmagloire1
    • one year ago
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    i accidentally checked the first one. an explanatoion would be great@

  3. jim_thompson5910
    • one year ago
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    have you learned about left hand limits? and right hand limits?

  4. tmagloire1
    • one year ago
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    yes

  5. jim_thompson5910
    • one year ago
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    so you know what this notation means? \[\LARGE \lim_{x \to 1^{-}} f(x)\]

  6. tmagloire1
    • one year ago
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    yes the limit is approaching 1 from the left side

  7. jim_thompson5910
    • one year ago
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    correct

  8. jim_thompson5910
    • one year ago
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    which piece will be used here? the x^2 + 4 piece? or the x+4 piece?

  9. tmagloire1
    • one year ago
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    x^2+4

  10. jim_thompson5910
    • one year ago
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    yes because f(x) = x^2 + 4 if x < 1

  11. jim_thompson5910
    • one year ago
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    so what we do is simply plug in x = 1 to get f(1) = 1^2 + 4 = 1+4 = 5 as x gets closer and closer to 1 from the left side, the limiting value is 5 in other words, \[\LARGE \lim_{x \to 1^{-}} f(x) = 5\]

  12. tmagloire1
    • one year ago
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    so it would be c because it doesn't equal 1?

  13. jim_thompson5910
    • one year ago
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    well let's compute the right hand limit

  14. jim_thompson5910
    • one year ago
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    do you know how to do so?

  15. tmagloire1
    • one year ago
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    The limit as x approaches 1 from the right side and plus in x=1 into x+4 ?

  16. jim_thompson5910
    • one year ago
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    yes because f(x) = x+4 when x > 1

  17. tmagloire1
    • one year ago
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    plug in*

  18. tmagloire1
    • one year ago
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    ok ill try it

  19. tmagloire1
    • one year ago
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    It also = 5 from the right side

  20. jim_thompson5910
    • one year ago
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    yes, \[\LARGE \lim_{x \to 1^{+}} f(x) = 5\]

  21. jim_thompson5910
    • one year ago
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    because f(1) is defined, and because the left and right hand limits equal the same value, this means f(x) is continuous at x = 1. It's continuous everywhere else because the two pieces are polynomials. All polynomials are continuous.

  22. tmagloire1
    • one year ago
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    so then it would be continuous

  23. jim_thompson5910
    • one year ago
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    actually wait...f(1) isn't defined

  24. jim_thompson5910
    • one year ago
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    I'm not thinking

  25. jim_thompson5910
    • one year ago
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    the piecewise function is set up in a way where x = 1 is left out

  26. jim_thompson5910
    • one year ago
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    notice how there are NO underlines under the > or the <

  27. tmagloire1
    • one year ago
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    Ohh i didnt notice that either

  28. jim_thompson5910
    • one year ago
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    f(x) = x^2 + 4 if x < 1 OR f(x) = x + 4 if x > 1 but what if x = 1 ? The function doesn't say, so f(1) is undefined

  29. tmagloire1
    • one year ago
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    Okay, thank you for explaing this problem i appreciate it!

  30. jim_thompson5910
    • one year ago
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    you're welcome

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