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Interesting problem i came acrosss 
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#1
Oct2013, 06:33 AM

P: 16

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=(x2)^2, i would easily do it. let A be angle b/w them, then, tanA= [tan(m1)tan(m2)]/1tanm1.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
Oct2013, 06:35 AM

P: 16

a small addendum, what i actually mean by angle b/w curves is the angle b/w their tangents at that point.



#3
Oct2013, 06:38 AM

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P: 12,016

a^(x)=b^(x)>(a/b)^x=1.
What does that tell you x must be, when "a" does not equal "b"? 


#4
Oct2013, 06:49 AM

P: 16

Interesting problem i came acrosss
you tell me, is there something wrong with this problem?



#5
Oct2013, 06:50 AM

P: 16

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



#6
Oct2013, 06:51 AM

P: 16

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. 


#7
Oct2013, 06:52 AM

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That's right!
Both functions equal 1 when x=0 


#8
Oct2013, 06:52 AM

P: 16

i'm not this dumb usually, its just that i got stuck here. thanks a lot.



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