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Math Help - Calculus assignment

  1. #1
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    Calculus assignment

    I'm doing an assignment on trig derivatives, limits, and graphing. I have no clue how to do this question though...

    the limit as x approaches 0 of:

    (tanx - sinx)/( x^2tanx)

    ps. sorry if you don't understand my question. I don't understand how to use that math font beyond exponents.
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by CenturionMonkey View Post
    I'm doing an assignment on trig derivatives, limits, and graphing. I have no clue how to do this question though...

    the limit as x approaches 0 of:

    (tanx - sinx)/( x^2tanx)

    ps. sorry if you don't understand my question. I don't understand how to use that math font beyond exponents.
    mult the top and bottom by 1/tanx to get

    \frac{1-\frac{\sin(x)}{\tan(x)}}{x^2}=\frac{1-\cos(x)}{x^2}

    there are a few ways to take this limit as x goes to zero the cool way is to expand cos as its power series

    \frac{1-(1-\frac{x^2}{2!}+\frac{x^4}{4!}-...)}{x^2}=\frac{\frac{x^2}{2!}-\frac{x^4}{4!}+...}{x^2}=\frac{\frac{1}{2}-\frac{x^2}{4!}+...}{1}

    taking the limit as x goes to zero gives 1/2

    or we could use L'hospitals rule

    we have the zero over zero form taking the derivatives we get


    \frac{1-\cos(x)}{x^2}=\frac{\sin(x)}{2x}

    use L.H again


    \frac{1-\cos(x)}{x^2}=\frac{\sin(x)}{2x}=\frac{\cos(x)}{2}

    taking the lim as x goes to zero gives 1/2 again.

    Good luck.
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  3. #3
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    i'm thankful for your time guys, but i'm sorry i have no clue what L'hospital's rule is. We were just given 4 formulas

    The limit as x approaches zero of:
    sinx=0
    cosx=1
    (sinx)/(x)=1
    (cosx - 1)(x)=0

    and we are expected to solve these with those formulas. We can also use the other formulas we learned last year. i.e. double-angle formulas, addition/subtraction formulas...etc.

    Thanks again
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Pennsylvania
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    Quote Originally Posted by CenturionMonkey View Post
    i'm thankful for your time guys, but i'm sorry i have no clue what L'hospital's rule is. We were just given 4 formulas

    The limit as x approaches zero of:
    sinx=0
    cosx=1
    (sinx)/(x)=1
    (cosx - 1)(x)=0

    and we are expected to solve these with those formulas. We can also use the other formulas we learned last year. i.e. double-angle formulas, addition/subtraction formulas...etc.

    Thanks again
    Look at this http://www.mathhelpforum.com/math-he...orial.html...I show how to use it
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