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Interesting problem i came acrosss

  1. Oct 20, 2013 #1
    okay,
    there are two curves: curve1: y=a^x and curve2: b^x. what is the angle between them at their point of intersection. given that (a≠b).
    My general method:
    if i wanted angle b/w the curves y=x^2 and y=(x-2)^2, i would easily do it.
    let A be angle b/w them,
    then, tanA= [tan(m1)-tan(m2)]/1-tanm1.tanm2
    can be used at their point of intersection.this is what my textbook says. but the problem with a^x and b^x is that I CANNOT FIND THE POINT OF INTERSECTION. which brings me to the very basic question, how can we find pt of intersection of curves like this?
     
  2. jcsd
  3. Oct 20, 2013 #2
    a small addendum, what i actually mean by angle b/w curves is the angle b/w their tangents at that point.
     
  4. Oct 20, 2013 #3

    arildno

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    a^(x)=b^(x)-->(a/b)^x=1.
    What does that tell you x must be, when "a" does not equal "b"?
     
  5. Oct 20, 2013 #4
    you tell me, is there something wrong with this problem?
     
  6. Oct 20, 2013 #5
    beacuse, at the same x point, a and b has to be equal to get you to the same y value as the equation suggests
     
  7. Oct 20, 2013 #6
    oh wait, i got it, x mustt be zero, so that for diff values of a and b, they get you the same y value.
    i got it now.
     
  8. Oct 20, 2013 #7

    arildno

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    That's right!
    :smile:
    Both functions equal 1 when x=0
     
  9. Oct 20, 2013 #8
    i'm not this dumb usually, its just that i got stuck here. thanks a lot.
     
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