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Math Help - Limits Involving Trigonometric Functions

  1. #1
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    Limits Involving Trigonometric Functions

    I am reviewing for my midterm and realize that I was out sick when the class covered trigonometric functions. Any explanation on how to solve these would be great!
    -limx->0 (x/arcsinx)
    -limx->infinity (xarccotx)
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by amm345 View Post
    I am reviewing for my midterm and realize that I was out sick when the class covered trigonometric functions. Any explanation on how to solve these would be great!
    -limx->0 (x/arcsinx)
    -limx->infinity (xarccotx)
    Hint:

    \frac{1}{f'(x)}

    and

    Let x=\frac{1}{z}.
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  3. #3
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    how about using L'Hospital's rule? that makes it a lot easier. by the way wats the answer.is the first one =1???
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  4. #4
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    I thought the first one was 0? and I already tried L'Hopitals and I still couldn't figure out.
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  5. #5
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    u need to differentiate the numerator and the denominator separately.then the numerator becomes 1.and the denominator becomes 1/sqrt(1-x^2).now put the limits and u should get 1.
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  6. #6
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    How about when I can't do it seperately?
    Like for limx->0 x/arccosx?
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  7. #7
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    i donot get the second one. limit doesnot exist for the second one unless x->0.
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  8. #8
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    x does tend to 0, isn't the limit equal to 0?
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  9. #9
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    no. limit for the second one is also 1.provided ,ofcourse,if x->0.
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  10. #10
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    u must learn your differentiation formulas well.
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