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Homework Help: Limits with trigs

  1. May 28, 2014 #1
    I am having trouble solving limits with trig functions.

    limx→0 x+xcosx/sinxcosx

    useful equation limθ→0 sinθ/θ = 1

    my attempt


    x/sinxcosx + xcosx/sinxcosx

    x/sinx*1/cosx + x/sinx this is where I am getting stuck
  2. jcsd
  3. May 28, 2014 #2


    Staff: Mentor

    the answer is right in front of you.

    As x approaches zero then what is the value of cosx?

    and you have the sinx/x as x approaches zero so everything is there for you
  4. May 28, 2014 #3

    Does x/sinx = 1 also?

    I thought sinx had to be in the numerator for it to = 1
  5. May 28, 2014 #4
    Technically, you're right. But note that if ##x\neq 0##, then ##\frac{x}{\sin x}=\frac{1}{\frac{\sin x}{x}}##, and you have something to which you can apply your limit law for ratios.

    So I guess technically you're not right (with regard to the value of the limit), but it's good to be skeptical. I had some students a year or so ago that got marked down (per a grading rubric that was not mine) for omitting the step that I showed.
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