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anonymous

  • 4 years ago

Is this a contradiction? On this problem they ask: Use the definitions of the hyperbolic functions to find the following limit: lim x->infinity sinhx However the answer is either: lim x->0^- coth(x) = -infinity or lim x->0^+ coth(x) = infinity Anyone see what I'm doing wrong? I'm attaching the original problem

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  1. anonymous
    • 4 years ago
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  2. anonymous
    • 4 years ago
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    Any ideas?

  3. anonymous
    • 4 years ago
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    i'm not sure what you're asking...

  4. anonymous
    • 4 years ago
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    are you sure the put the right attachment

  5. anonymous
    • 4 years ago
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    I'm sorry, my bad, mistyped the uploaded file

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  6. anonymous
    • 4 years ago
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    I'll take that as no one is sure what to do...

  7. anonymous
    • 4 years ago
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    do you know the standard algebraic expressions for the hyperbolic functions?

  8. anonymous
    • 4 years ago
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    x = sinh x = (e^x - e^-x)/2

  9. anonymous
    • 4 years ago
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    * sinhx = sinh x = (e^x - e^-x)/2

  10. campbell_st
    • 4 years ago
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    well use the definition \[\sinh (x) = (e^x - e^(-x))/2\] so its the \[\lim_{x \rightarrow \infty} (e^x - e^(-x))/2\] rewriting \[\lim_{x \rightarrow \infty} e^x/2 - \lim_{x \rightarrow \infty} 1/(2e^x)\] 2nd part approaches 0 as x approaches infinity 1st part has approaches infinity

  11. anonymous
    • 4 years ago
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    Ah, I see, thats kind of a strange problem

  12. anonymous
    • 4 years ago
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    thanks!

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spraguer (Moderator)
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