Find the constant k that will make this piecewise continuous.

  1. 1. The problem statement, all variables and given/known data
    Find a value for the constant k that will make the function below continuous:

    [itex]f(x)=\frac{x-1}{x^2-1}\ \text{if}\ x<=0[/itex]
    [itex]f(x)=\frac{tankx}{2x}~\text{if}~x>0[/itex]



    2. Relevant equations



    3. The attempt at a solution
    I've tried the only solution I can think of, which is to make
    [itex]\frac{x-1}{x^2-1} = \frac{tankx}{2x}[/itex]

    And then I plug in 0 to try and get k, but I end up with 1 = 0/0. I know you are supposed to do something to the second equation to remedy this, but I cannot figure out what. I am fairly new to Calculus, so some help would be greatly appreciated.
     
  2. jcsd
  3. SammyS

    SammyS 8,765
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    Hello kaderyo94. Welcome to PF !

    Each piece of this piecewise-defined function has one or more discontinuities in its portion of the domain of the overall function. You can't "fix" those discontinuities by a choice of k.

    I suspect the problem is: Find a value for the constant k that will make the function continuous at x = 0, which is where the two "pieces" join.

    If that's the problem to be solved, then:

    What must be true for the following limit to exist?
    [itex]\displaystyle \lim_{x\to\,0}\,f(x)[/itex]​
    Then, how must that limit be related to f(0) ?
     
  4. HallsofIvy

    HallsofIvy 40,678
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    You titled this "Find the constant k that will make this piecewise continuous" but then said "Find a value for the constant k that will make this function continous". Those are very different!
     
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