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Indeterminate forms

  1. Jan 2, 2015 #1
    What is the right hand and left hand limit of (sinx)^tanx?
    I know this is an indeterminate form 0^0 but what are the RHL and LHL because though I intuitively know that 0^0 is indeterminate, I don't understand what the right hand and left hand limits are?
  2. jcsd
  3. Jan 2, 2015 #2
    As I implement!!

    $$\lim_{x\rightarrow 0}sinx^{tanx}$$

    look at the graph of the function

    http://www.wolframalpha.com/input/?i=sin x^{tan x}

    And this is intuitively reasonable,
    Let us assume a very small value approaching to zero for theta [in radians] , say 0.00000001, then the value will be very close to 1
    This is the limit from the right .
    And the limit from the lift doesn't exist since you x^x is not always valid for negative numbers..,

    Hope that is right and what you are looking for ,,
    Last edited: Jan 2, 2015
  4. Jan 3, 2015 #3


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    It doesn't make sense to talk about "limits" at all without saying what x itself if going to. I presume here you mean "limit as x goes to 0". The "left hand limit" would be as x approaches 0 "from the left" on the number line- that is, x is always negative. The "right hand limit" would be as x approaches 0 "from the right on the number line- x is always positive.

    You should be able to see from your graph that if x is approaching 0 "from the right" or "from above", then f(x) goes to 1 while it cannot approach 0 "from the left" or "from below" because, as Maged Saeed said, sin(x)tan(x) is not defined there.
  5. Jan 6, 2015 #4
    Ok thanks :D
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