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!

Evaluate lim e^x when x approaches zero from negative

  1. Jan 2, 2013 #1
    1. The problem statement, all variables and given/known data
    What is the limit of e^x when x approaches zero from negative side


    2. Relevant equations



    3. The attempt at a solution
    Taylor series? Then the answer is put all x= 0 , and the answer is 1, but why the question ask from negative side??

    Thank you very much
     

    Attached Files:

    • am.PNG
      am.PNG
      File size:
      459 bytes
      Views:
      86
  2. jcsd
  3. Jan 2, 2013 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Can you use that e^x is continuous? This would allow to use e^0.
    If not, what do you know about the exponential function?

    That is a strange question.
     
  4. Jan 2, 2013 #3
    The question didn't say, but if it is continuous then I can use Taylor series for e^x . Then just substitute all x with zero? And get answer 1 . Then what is the point to have x approaches zero? Or should I use graph ?
    Thank you
     
  5. Jan 2, 2013 #4

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    What are the *definitions* of e and e^x that you are allowed to use? What facts about e^x are you allowed to use? The point is: how you deal with the problem depends crucially on what properties of e^x you know already. The question you present is almost meaningless, because you leave out so much important information.
     
  6. Jan 2, 2013 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    It is not sufficient for a function to be continuous in order that it HAVE a Taylor series. But the Taylor series has nothing to do with the question.

    Do you understand what "continuous" means? The definition of "continuous" is that that the limit, as x goes to a, is equal to the value of the function, f(a). That is the point of "x approaches 0"- you evaluate the function at x= 0. If you meant to ask "why approach 0 from the negative side" there doesn't appear to be any special reason except perhaps to see if you really understood the idea of "limit". If f(x) is continuous at x= a (and e^x is continuous for all x), then, by definition, [itex]\lim_{x\to a} f(x)= f(a)[/itex], and, if the limit exists, [itex]\lim_{x\to a^-}f(x)= \lim_{x\to a^+} f(x)= \lim_{x\to a} f(x)[/itex].
     
  7. Jan 2, 2013 #6
    Well e^x is differentiable therefore continuous at 0. So the limit at left of 0 is the same as the right of 0.
     
  8. Jan 2, 2013 #7
    Thank you guys.

    This is the whole question that I get from past year exam .
    Evaluate lim e^x when x approaches zero from negative.

    Thank you . I am too eager to solve problem until forget all the important basic knowledge.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Evaluate lim e^x when x approaches zero from negative
  1. E^x + x = c (Replies: 6)

  2. Lim{x->0} function (Replies: 21)

  3. E^x+x = 5 (Replies: 4)

  4. E^-x, solve for x (Replies: 5)

Loading...