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anonymous

  • 5 years ago

lim at 0 of r^2*ln(r^2)?

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  1. anonymous
    • 5 years ago
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    Is this lim as r approaches 0? All you need to do for this one is plug 0 into all r's. r^2*ln(r^2)? (0)^2*ln((0)^2) = DNE

  2. anonymous
    • 5 years ago
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    The limit is as r approaches 0+, but the answer is supposed to be 0 and I just can't prove it...

  3. anonymous
    • 5 years ago
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    This is an indeterminate of the form 0^(0) so try using L'Hopitals Rule

  4. anonymous
    • 5 years ago
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    my mistake its actually (-infinity)^(0) but still and indeterminate, so L'Hopitals should work

  5. anonymous
    • 5 years ago
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    the answer is 0

  6. anonymous
    • 5 years ago
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    does anyone want the method

  7. anonymous
    • 5 years ago
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    yes please!

  8. anonymous
    • 5 years ago
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    can nobody please explain to me how to apply de l'hopital to this? or any other method?

  9. anonymous
    • 5 years ago
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    hello friend, it was my mistake. I thought it was r^2/ln(r^2)?

  10. anonymous
    • 5 years ago
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    else the answer is infinity. I can explain you the L'hospital rule

  11. anonymous
    • 5 years ago
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    If you get 0^0 form or 0/0 then you can differentiate the given function which is r^2*ln(r^2) here

  12. anonymous
    • 5 years ago
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    when u find d/dr(r^2*ln(r^2) the answer is 2rln(r^2)+2r

  13. anonymous
    • 5 years ago
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    this is again of the form 0^0 therefore u differentiate it again

  14. anonymous
    • 5 years ago
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    so u wud get 2ln(r^2)+6 which is again log0=infinity, when r tends to 0

  15. anonymous
    • 5 years ago
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    again u differentiate it, u wud get 4/r when r tends to zero, 4/r wud tend to infinity as any number divided by 0 is infinity

  16. anonymous
    • 5 years ago
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    therefore u wud get an infinity

  17. anonymous
    • 5 years ago
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    okay

  18. anonymous
    • 5 years ago
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    but wouldn't the limit of 2ln(r^2)+ 6 be -infinity?

  19. anonymous
    • 5 years ago
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    so u can again differentiate

  20. anonymous
    • 5 years ago
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    when u differentiate it again and again and again, u r getting only infinity.differentiating means breaking into smaller parts. But when we add this delta x and delta y again and again we are still getting infinity so the answer wud be infinity

  21. anonymous
    • 5 years ago
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    yes but 50% of the time its -inf and the other 50% its +inf.. so which one is the right answer?

  22. anonymous
    • 5 years ago
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    nope its not -infinity, when u differentiate for the fourth, fifth, sixth and so on u wud only get +infinity apart from the 3 differentiation

  23. anonymous
    • 5 years ago
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    so ur answer is DNE

  24. anonymous
    • 5 years ago
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    Thanks Dipin!

  25. anonymous
    • 5 years ago
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    ur welcome

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