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Limit trouble

  1. Jan 22, 2007 #1
    1. The problem statement, all variables and given/known data
    a.\lim_x -->infty arctan(x^2-x^4) =
    b.\lim _x --->pi/2 e^tan (x) =

    2. Relevant equations
    Limit laws


    3. The attempt at a solution

    a. I know I can use the limit laws to take the limit of Arctan@infinity=1/2, but then, I don't know if I should factor out the (x^2-x^4)

    b. Don't even know.
     
    Last edited: Jan 23, 2007
  2. jcsd
  3. Jan 22, 2007 #2
    a. x^2-x^4 approaches negative infinity as x approaches positive infinity.

    b. Look at both sides of the limit.
     
  4. Jan 22, 2007 #3
    Ok, Im pretty sure b. is 0 because of the rule lim x-->infin e^X=0. We can substitute and look at the graph and it is 0.

    Still not sure about a., taking the limit of Arctan@infinity=1/2 and (x^2-x^4) approaches -infinity so what then?
     
  5. Jan 22, 2007 #4
    What is arctan x as x approaches negative infinity? It is not 1/2.

    For b, consider that if the right and left sides of the limit don't agree, then there is no limit.
     
    Last edited: Jan 23, 2007
  6. Jan 23, 2007 #5
    I am looking as it approaches +infinity(sorry if I didn't specify) and I am positive it is 1/2. Basicaly [lim x->inf. arctan=1/2]*[lim x->inf. (x^2-X^4)=+infinity}
    right?
     
  7. Jan 23, 2007 #6

    Gib Z

    User Avatar
    Homework Helper

    Did you get the hint about b? Try tan 89.999 degrees in your calculator, then then 90.0001, what do you see?
     
  8. Jan 23, 2007 #7

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    You appear to be "positive" about several things that are not true!
    tan(1/2)= 0.5463, not infinity! Perhaps you forgot a [itex]\pi[/itex]?

    You also say
    There is no such rule. The limit, as x goes to infinity of ex is definitely NOT 0! Surely you have seen a graph of y= ex!
     
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