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Difficulty to find this limit

  1. Apr 22, 2012 #1
    Hello! I'm having difficulty to find this limit: [tex]\lim_{x\rightarrow -1}(\sqrt[3]{\frac{x^3+1}{x+1}})[/tex]
    This is what I'm trying to do to solve this limit: Let [tex]\frac{x^3+1}{x+1}=u[/tex] then
    [tex]\lim_{x\rightarrow -1}(\sqrt[3]{u}) = \lim_{x\rightarrow -1}(\sqrt[3]{-1})[/tex]

    I know something is wrong I'm just not sure about what is actually wrong. I'm thinking that [tex]\lim_{x\rightarrow -1}(\sqrt[3]{u})[/tex] Is wrong because that -1!

    Thanks!
     
  2. jcsd
  3. Apr 22, 2012 #2


    Hint: [itex]x^3+1=(x+1)(x^2-x+1)[/itex] .

    DonAntonio
     
  4. Apr 22, 2012 #3
    Also when you use the algebraic substitution, you need to consider the limit of the new variable u. So, as x--> -1 , what is the limiting value of u? However, this line of thiking will not save you from facing the indeterminate form (0/0). The easiest path is the hint that DonAntonio suggested.
     
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