Home > Math Group > Question and Answer

Math Group

Question:

pavelpimen
pavelpimen
Student
High School - 10th Grade

Considering functions f:R - R, f(x)= x/(1+x^2) and g:R - R, g(x)=arctgx calculate lim(f(x)g(x));x - infinite

Rate question:

Posted by pavelpimen on Monday May 25, 2009 at 5:51 AM and tagged with math.

Answers:

  1. giorgiana1976
    giorgiana1976 Teacher
    Doctorate

    eNotes Editor

    Best answer as selected by question asker.

    lim f(x)*g(x)=lim f(x)*lim g(x)

    lim x/(1+x^2)=lim x/ lim [x^2(1/x^2 + 1)]

    We'll reduce the fraction with x

    lim 1/ lim x* lim(1/x^2 + 1)]=1/infinity=0

    lim arctg x= arctg limx =arctg infinity= pi/2

    lim f(x)*lim g(x)= 0*pi/2=0

    Rate answer:

    Posted by giorgiana1976 on Monday May 25, 2009 at 7:58 AM