1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Evaluating a limit: e^tan x

  1. Oct 14, 2008 #1
    1. The problem statement, all variables and given/known data

    Evaluate the following limit. lim as x approaches Pi/2 + of etan x.

    2. Relevant equations

    None.

    3. The attempt at a solution

    Well I've graphed this and I know it approaches 0, but I don't know how to actually solve this. And I'm fairly sure I'm not allowed to just substitute a number close to Pi/2, unless thats the only way. Thanks!
     
  2. jcsd
  3. Oct 14, 2008 #2
    The limit is zero. Actually, you can go to the table on your calculator (2nd, graph) and type in numbers that are extremely close and that will work. The limit is what it approaches, in this case from the right, and it's 0.
     
  4. Oct 14, 2008 #3

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    The limit of tan(x) as x decreases to pi/2 is -infinity. To show that tan(x)=sin(x)/cos(x) and you probably know their limit around pi/2. Or just look at a graph of tan(x). Then just look at a graph of e^x as x->-infinity.
     
  5. Oct 14, 2008 #4
    Are you disagreeing with me? I can't tell what point you're trying to get across.

    The limit of e^tan(x) as x approaches pi/2 from the right is zero.
     
  6. Oct 14, 2008 #5

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    No, I'm agreeing with you. I'm just trying to say how to describe the problem without a calculator.
     
  7. Oct 15, 2008 #6
    Ok thanks. I already knew the answer, and I can explain it conceptually. I just thought there was a more, mathematical?, way of showing the answer.
     
  8. Oct 15, 2008 #7

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You can do epsilons and deltas if you want. I don't think that's necessary.
     
  9. Oct 15, 2008 #8
    Here is an informal way to think about it. The limit as x approaches pi/2+ of tan(x)= -infinity. e^(-infinity) = 1/(e^infinity) = 0.
     
  10. Oct 15, 2008 #9

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    ex and tan(x) are both continuous functions. [itex]tan(\pi/2)= 0[/itex] and e0= 1. Drum roll.
     
  11. Oct 15, 2008 #10

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    tan(pi/2)=0??? tan(x) continuous??????
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Evaluating a limit: e^tan x
  1. Limit of arctan(e^x)? (Replies: 3)

Loading...