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anonymous

  • 5 years ago

If the Limit of a function = L as x approaches c, does the f(c)= L? Explain?

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  1. amistre64
    • 5 years ago
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    well, that IS the definition .... so yes.

  2. amistre64
    • 5 years ago
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    If the limit if a function is the limit of a function; does the limit of the function exist? .... yes

  3. anonymous
    • 5 years ago
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    heck no

  4. amistre64
    • 5 years ago
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    youve pretty much asked: I circle is round if a circle is round; is a circle round? if so, why?

  5. anonymous
    • 5 years ago
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    if it did, why would you say limit?

  6. amistre64
    • 5 years ago
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    i see it lol

  7. anonymous
    • 5 years ago
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    you would just say \[f(c)\]

  8. anonymous
    • 5 years ago
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    How about if f(c) = L, then the limit of f(x) as x approaches c = L?

  9. amistre64
    • 5 years ago
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    f(c) doesnt HAVE to equal L; but that is the gist of it

  10. amistre64
    • 5 years ago
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    semantics lol

  11. anonymous
    • 5 years ago
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    right that is the whole point. if you could compute limits by evaluating functions we would never have heard of them.

  12. anonymous
    • 5 years ago
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    Well, the book is telling me it is false.........

  13. anonymous
    • 5 years ago
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    of course it is false!

  14. anonymous
    • 5 years ago
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    that is the whole point. if the function is continuous then it is true.

  15. amistre64
    • 5 years ago
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    the limit if a poly is L at c :)

  16. anonymous
    • 5 years ago
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    here is the simplest example i can think of \[lim_{x->2}\frac{x^2-4}{x-2}\]

  17. anonymous
    • 5 years ago
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    in this case \[f(x)=\frac{x^2-4}{x-2}\] and this limit is obviously 4 but \[f(4)\] is undefined.

  18. amistre64
    • 5 years ago
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    oh that aint the simplest lol; how about: x^2 --- as x approaches 0 x

  19. anonymous
    • 5 years ago
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    ok simpler still.

  20. anonymous
    • 5 years ago
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    I think a piecewise function would be a better explanation....

  21. anonymous
    • 5 years ago
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    matter of fact here is an even simpler one. \[f(x)=x\] if \[x\neq5\] \[f(5)=\pi\]

  22. amistre64
    • 5 years ago
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    piecewise is better suited for continuity i think

  23. anonymous
    • 5 years ago
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    then the limit as x->5 is 5, but \[f(5)=\pi\]

  24. anonymous
    • 5 years ago
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    no i don't think piecewise is a better explanation at all.

  25. anonymous
    • 5 years ago
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    well except that my example was a piecewise function.

  26. anonymous
    • 5 years ago
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    Ok, it was a little tricky at first, but it is actually pretty simple..........thanks satellite

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