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anonymous

  • one year ago

Continuity and One-sided limits

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  1. anonymous
    • one year ago
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    \[ \lim_{x \rightarrow 1} f(x) (1- ||-\frac{ x }{ 2 }||)\]

  2. anonymous
    • one year ago
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    Hi, I can help you!

  3. anonymous
    • one year ago
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    thanks

  4. anonymous
    • one year ago
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    Just to check, first, is this meant to be a one-sided limit? And if so, which side of 1 are we approaching from?

  5. anonymous
    • one year ago
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    here let me take a pic of the problem in my textbook

  6. anonymous
    • one year ago
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    Okay, sure. (If it's any easier, what I'm basically asking is whether there's a little + sign or a little - sign next to the "x->1")

  7. anonymous
    • one year ago
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    oh, it is just 1

  8. anonymous
    • one year ago
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    Okay, cool.

  9. anonymous
    • one year ago
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    Well, were taking the limit as x gets close to 1. So let's stick that into the equation.

  10. anonymous
    • one year ago
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    http://i.imgur.com/hlnt6Lg.jpg number 26

  11. anonymous
    • one year ago
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    i would get 1 1/2 ?

  12. anonymous
    • one year ago
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    Well, the bit inside the ||#|| symbol should always be positive, right?

  13. anonymous
    • one year ago
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    I mean, it's an absolute value symbol, if I understood right. So ||5|| = +5, and ||-7|| = +7.

  14. anonymous
    • one year ago
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    In this case, you'd want ||-x/2|| to be positive

  15. anonymous
    • one year ago
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    Did you click the link? it isn't an absolute value sign

  16. anonymous
    • one year ago
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    Oops, my bad!

  17. anonymous
    • one year ago
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    its alright, kinda hard to input calc equations through text, not all the symbols are included

  18. anonymous
    • one year ago
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    Looks like it's the floor function then, which takes whatever is inside it and rounds it down to the nearest integer.

  19. anonymous
    • one year ago
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    so if x->1 then -x/2 becomes -1/2, which becomes -1 once you apply the floor function, and then you have 1 - (-1) which is 2. Does that sound sensible?

  20. anonymous
    • one year ago
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    how does -1/2 become 1 instead of 0?

  21. anonymous
    • one year ago
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    Looking at that photo again, I'm a bit confused because that notation is a bit different to what I normally use for the floor function. Maybe we want round-to-the-nearest-integer, rather than round-down-to-the-next-integer?

  22. anonymous
    • one year ago
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    Is it because it is as x approaches 1 from the right and left, so i wouldn't include 0 or 2 ? other wise it would be, as x approaches 0 from the right and as x approaches 2 from the left right?

  23. anonymous
    • one year ago
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    @BasketWeave

  24. anonymous
    • one year ago
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    Hmm. I'm a bit confused, to be honest. I think I'd better admit that right now rather than accidentally give you the wrong answer.

  25. anonymous
    • one year ago
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    Sorry! :(

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