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A Close Match
Can you massage the parameters of these curves to make them match as closely as possible?
Age 16 to 18
Challenge Level
I asked my integrating application to work out this integral:
Integrate[1000000/(10 + (1000000 - 10)/2^(4*x)), x]
I was given the answer
(25000*Log[-32*(99999 + 16^x)])/Log[2]
Try to evaluate this expression at $x=1$. What has gone wrong? Can you work out the actual real answer and verify by differentiation?
Did you know ... ?
Technology is undoubtedly a very useful mathematical tool, but needs to be used carefully and with some skepticism. If you use a calculating aid it is very important to check that the answer makes sense. Algebraic tools tend not to make errors, but often introduce unnecessary complexity into an answer.
Technology is undoubtedly a very useful mathematical tool, but needs to be used carefully and with some skepticism. If you use a calculating aid it is very important to check that the answer makes sense. Algebraic tools tend not to make errors, but often introduce unnecessary complexity into an answer.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.