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Continuity math homework

  1. Sep 3, 2013 #1
    1. The problem statement, all variables and given/known data

    f(x) = [1 - tan(x)]/[1 - √2 sin(x)] for x ≠ π/4
    = k/2 for x = π/4

    Find the value of k if the function is continuous at x = π/4

    3. The attempt at a solution

    This means that lim x → π/4 f(x) = k/2

    I put x = (π/4 + h) and then evaluated the limit as h tended to zero. Doesn't work. Get sin (2h) in the denominator. Can I get a hint?
     
  2. jcsd
  3. Sep 3, 2013 #2

    Zondrina

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    Homework Helper

    You should check both sides of the limit using ##\frac{1 - tan(x)}{1 - \sqrt{2} sin(x)}##.

    This will allow you to figure out what ##k## must be in order for the function to truly be continuous at ##x = \pi/4##.
     
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