1. Limited time only! Sign up for a free 30min personal 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!

Definition of tangent line

  1. Mar 15, 2015 #1
    1. The problem statement, all variables and given/known data

    My textbook says that the slope of the tangent line at a point can be expressed as a limit of secant lines:

    [tex]
    m = \underset{x \rightarrow a}{\lim} \, \frac{f(x) - f(a)}{x - a} \, .
    [/tex]

    If x > a and we approach a from the right, why do we have to insist that this limit exists? Why can't we settle for the right-handed limit instead?

    2. Relevant equations


    3. The attempt at a solution

    I'm really not sure why the left limit needs to exist. Any help is appreciated.
     
  2. jcsd
  3. Mar 15, 2015 #2
    Because sometimes the left limit is different from the right limit. Then the limit doesn't exist, and you don't have any one tangent line. Look at the function [tex]f(x) = |x|[/tex] at [itex]x = 0[/itex]. What is the left hand tangent line limit? What's the right one?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Definition of tangent line
  1. Tangent Line (Replies: 4)

  2. Tangent Line (Replies: 6)

  3. Tangent lines (Replies: 1)

  4. Tangent of a line (Replies: 14)

  5. Tangent line (Replies: 4)

Loading...