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anonymous

  • 4 years ago

if x approaching 3 from the left =22 and x approaching 3 from the right = 22 but the lim f(x) as x approaches 3 = 20. is the function continuous at x=3? why or why not

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  1. anonymous
    • 4 years ago
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    ? if the limit from the left is 22 and the limit from the right is 22, then the "limit' cannot be 20

  2. anonymous
    • 4 years ago
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    im given a piecewise

  3. anonymous
    • 4 years ago
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    f(x)= 2x^2 +4 when x<3 20 when x=3 28-2x when x>3

  4. anonymous
    • 4 years ago
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    and im asked to find the limit of x to 3+ x to 3- x to 3

  5. anonymous
    • 4 years ago
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    piecwise or not, if \[\lim_{x\rightarrow 3^-}f(x)=22=\lim_{x \rightarrow 3^+}f(x)\] then the limit is 22, not something else

  6. UnkleRhaukus
    • 4 years ago
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    the function is not continuous at the point x=3

  7. anonymous
    • 4 years ago
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    ah the limit is 22, but the function is not continuous at 3 because it is not the same as the value of the limit there

  8. anonymous
    • 4 years ago
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    why is that unklerhaukus

  9. anonymous
    • 4 years ago
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    for the function to be continuous, it must have the same value as the limit

  10. anonymous
    • 4 years ago
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    so since \[\lim_{x\rightarrow 3} f(x)=22\] but \[f(3)=20\] it is not continuous at 3

  11. anonymous
    • 4 years ago
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    ok

  12. UnkleRhaukus
    • 4 years ago
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    Satellite73 has already said this but The function is Only continuous at some point if the limit Exists And is Equal to the function at that point.

  13. anonymous
    • 4 years ago
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    ok can you help me with this one state the definition of a function f(x) which is continuous at x= a

  14. anonymous
    • 4 years ago
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    Yes, actually this (following) statement is pretty confusing "the lim f(x) as x approaches 3 = 20."

  15. anonymous
    • 4 years ago
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    i was wrong there

  16. anonymous
    • 4 years ago
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    A function is continuous at x=a if \[ \large \space \lim \limits_{x\rightarrow a^-}f(x)=f(a)=\lim \limits_{x \rightarrow a^+}f(x) \]

  17. UnkleRhaukus
    • 4 years ago
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    (assuming the limit exists of course)

  18. anonymous
    • 4 years ago
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    If \( \space \lim \limits_{x\rightarrow a^-}f(x)=\lim \limits_{x \rightarrow a^+}f(x) \) then the limit exists.

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