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Arctan limit (without L'Hopital's Rule)

  1. Sep 28, 2016 #1
    1. The problem statement, all variables and given/known data
    Limx-->positive infty arctan(1+x)/(1-x)

    2. Relevant equations


    3. The attempt at a solution
    I just need to know if my answer is right.

    Knowing that when the leading coefficients of the x when its the same, then the answer is just the ratio. So it would be -1. Then in my calculator I put arctan -1 and it gave -45. Is this right?
     
  2. jcsd
  3. Sep 28, 2016 #2

    Mark44

    Staff: Mentor

    In math problems, trig functions and their inverses are usually in radians. Your calculator is set to degree mode. The book's answer will almost certainly be in radians. Otherwise, your value of -1 is correct.
     
  4. Sep 28, 2016 #3
    The answer is not in the book. My book has a weird way of giving the answers. Only gives for odd numbered questions and this ones an even so I have no way of knowing if my answer is right.

    So instead of -45 it would be -pi/4 ?
     
  5. Sep 28, 2016 #4

    Ray Vickson

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    Science Advisor
    Homework Helper

    Do you mean
    $$\frac{\arctan(1+x)}{1-x}$$
    or do you mean
    $$\arctan \left( \frac{1+x}{1-x} \right)?$$
    If you mean the latter you need parentheses, like this: arctan((1+x)/(1-x)) or arctan[(1-x)/(1+x)].
     
  6. Sep 28, 2016 #5

    Mark44

    Staff: Mentor

    That's not at all unusual for math books. If the answer you get for an odd-numbered problem agrees with the book's answer, you can have some confidence that your work for a nearby even-numbered problem is also correct.

    Right.

    I agree completely. I assumed from the answer given by the OP, that the problem was as you show it here, Ray.
     
  7. Sep 28, 2016 #6

    Ray Vickson

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    I agree that we can try to guess the meaning by looking at what the OP has done; but the OP needs to realize that clearer communication is important.
     
  8. Sep 28, 2016 #7

    Mark44

    Staff: Mentor

    Absolutely.
     
  9. Sep 28, 2016 #8

    Its the second one , but in my original post thats exactly how I entered it.
     
  10. Sep 28, 2016 #9
    Okay I just noticed I actually put two brackets. I can see now why everyone is confused and guessing. Thanks for correction.
     
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