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Math Help - I need help to find the value of " m " (variable)

  1. #1
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    I need help to find the value of " m " (variable)

    In this function y = {sin2x/x (for x no 0), and m-1 (for x=0) } find the value of m that function y to be countinous in x=0.
    Can anybody help me with this?
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  2. #2
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    Re: I need help to find the value of " m " (variable)

    I'm not sure how advanced your definition of continuity is. In the most elementary terms, a function is continuous at a point b if 1) the limit of the function at b exists and 2) it equals f(b).

    You can see that f(x)= \frac{sin(2x)}{x} has a removable discontinuity at x=0. So, the limit exists at 0, but the actual value of the function is undefined (because that pesky x in the denominator becomes zero, and dividing by zero is undefined). So, if we simply define f(0)=2=m-1, we have defined the function so that the limit at 0 exists, and the function takes on the value of the limits. So, m=3.
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  3. #3
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    Re: I need help to find the value of " m " (variable)

    Quote Originally Posted by reobjan View Post
    In this function y = {sin2x/x (for x no 0), and m-1 (for x=0) } find the value of m that function y to be countinous in x=0.
    Hint: {\lim _{x \to 0}}\frac{{\sin (x)}}{x} = 1 so {\lim _{x \to 0}}\frac{{\sin (2x)}}{x} = ~?
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  4. #4
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    Re: I need help to find the value of " m " (variable)

    Just a little more:
    {\lim _{x \to 0}}\frac{{\sin (x)}}{x} = 1 so {\lim _{x \to 0}}2\frac{{\sin (2x)}}{2x} = ~?[/QUOTE]
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