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Math Help - Limits of Trig Functions

  1. #1
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    Limits of Trig Functions

    I've been working on this problem for a long time now and I haven't been able how to figure it out. It is:

    lim sin x/x+tan x *as x approaches 0*
    The answer is 1/2 but i dont understand how to get there
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  2. #2
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    Consider \lim_{x\to 0 }\frac{\sin x }{x} = 0
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  3. #3
    Junior Member autumn's Avatar
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    Quote Originally Posted by pickslides View Post
    Consider \lim_{x\to 0 }\frac{\sin x }{x} = 0
    YOU mean 1 not 0
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  4. #4
    Senior Member DeMath's Avatar
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    Quote Originally Posted by mhuggin2 View Post
    I've been working on this problem for a long time now and I haven't been able how to figure it out. It is:

    lim sin x/x+tan x *as x approaches 0*
    The answer is 1/2 but i dont understand how to get there
    Divide the numerator and denominator by x

    \lim_{x\to0}\frac{\sin{x}}{x+\tan{x}}=\lim_{x\to0}  \frac{\dfrac{\sin{x}}{x}}{1+\dfrac{1}{\cos{x}}\cdo  t\dfrac{\sin{x}}{x}}=\frac{1}{1+\dfrac{1}{1}\cdot1  }=\frac{1}{2}.
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  5. #5
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    Quote Originally Posted by autumn View Post
    YOU mean 1 not 0
    yep, silly typo.
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  6. #6
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    Thanks

    OMG thank you SO much. It all makes so much sense now
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