Limit this?

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  • Alan
    Lv 7
    1 week ago

    correct that cos(1/x) tends toward one as 1 

    leaving 

     lim x-> -infinity   xe^(x)   

    but that can be rewritten as 

    x/(1/e^x)    which is  -infinity/infinity 

    so use l'hopital rule 

     1/  (-e^(-x)    =  -e^x 

    lim x-> -infinity   -e^(x) = -0 = 0  

    so the answer = 0     

       

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  • Vaman
    Lv 7
    1 month ago

     cos (1/x) when x tends to - infinity, is 1.e^(-x)+1-1= e^(-x)

    x e^(-x). e^(-x) tends to infinity faster when x tends to - infinity. Therefore, it is negative infinity

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