solve
posted by Jen .
e^c2c = e2
what is c?
ummm, 1?
e^1 = e
2*1 = 2
No! Answer is 0.351
How do I get this?
c = 1 is one solution. To find the other, you can proceed as follows.
e^c2c  e + 2 = 0
put f(c) = e^c2c  e + 2
Newton's Method (approximate functon by the tangent) gives succesive better and better approximations.
c_{n+1} = c_{n}  f(c_{n})/f'(c_{n})
= c_{n} 
[e^c_{n}2c_{n}  e + 2]/[e^c_{n}  2]
Take c_{1} = 0
then:
c_{2}=0.2817
c_{3}=0.3465
c_{4}= 0.351326
c_{5}= 0.351354757134
c_{6}= 0.351354758153
c_{6} is correct to 12 digits.
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