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Limits problem

  1. Jun 4, 2012 #1

    pcm

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    1. The problem statement, all variables and given/known data
    find:
    lim x[itex]\rightarrow0[/itex] (x+2)tan-1(x+2)-xtan-1(x)


    2. Relevant equations



    3. The attempt at a solution
    lim x[itex]\rightarrow0[/itex] (x+2)tan-1(x+2)-xtan-1(x)=
    lim x[itex]\rightarrow0[/itex] [x(tan-1(x+2)-tan-1(x))+2tan-1(x+2)]
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jun 4, 2012 #2

    LCKurtz

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    Science Advisor
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    Gold Member

    Your functions are all continuous. What happens if you plug in ##x=0##?
     
  4. Jun 4, 2012 #3

    pcm

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    ah sorry, its x[itex]\rightarrow∞[/itex]
     
  5. Jun 4, 2012 #4

    pcm

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    x(tan-1(x+2)-tan-1(x))
    this part can be evaluated using l hopital(?),but it requires multiple use of rule.
    i am expecting kind of trigonometric solution.
     
  6. Jun 4, 2012 #5
    Focus on the tan-1(x) and tan-1(x+2). What are their limits as x goes to infinity?
     
  7. Jun 4, 2012 #6

    pcm

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    both tends to π/2
     
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