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!

Squeeze Theorem/Limits Question. Answers don't match up.

  1. Jun 17, 2013 #1
    1. The problem statement, all variables and given/known data

    Evaluate using the Squeeze Theorem.
    [itex] \lim_{x\rightarrow0} (2^{x} - 1) cos\frac{1}{x} [/itex]

    2. Relevant equations



    3. The attempt at a solution

    [itex] -1 ≤ cos\frac{1}{x} ≤ 1 \\
    1 - 2^{x} ≤ (2^{x} -1)cos\frac{1}{x} ≤ 2^{x} - 1 \\
    0 ≤ (2^{x} -1)cos\frac{1}{x} ≤ 0 \\
    ∴ \lim_{x\rightarrow0} (2^{x} - 1) cos\frac{1}{x} = 0 [/itex]

    That's the solution I got and the solution that's in my textbook. But when I checked on wolframalpha, it says the limit does not exist.

    Did I do something wrong and is my textbook wrong? or is it something conceptually that I don't understand about this? Is wolframalpha wrong?
    Thanks :)
     
  2. jcsd
  3. Jun 17, 2013 #2

    Mark44

    Staff: Mentor

    It's possible that you inadvertently entered something different into wolfram. Your answer is correct.
     
  4. Jun 18, 2013 #3

    jbunniii

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You are correct that the limit is zero, but your reasoning has some flaws. The last line is clearly not correct, for it is equivalent to
    $$(2^x - 1)\cos\left(\frac{1}{x}\right) = 0$$
    which is not true for all ##x##. The previous line is correct, but only if ##2^x - 1 \geq 0##.

    It's somewhat easier to work with absolute values:
    $$\left|\cos\left(\frac{1}{x}\right)\right| \leq 1$$
    Now multiply both sides by ##|2^x - 1|## and see what you can conclude.
     
  5. Jun 19, 2013 #4

    for x < 0, this statement is false.
     
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: Squeeze Theorem/Limits Question. Answers don't match up.
  1. Squeeze Theorem Limit (Replies: 5)

Loading...