### Weekly Challenge 43: A Close Match

Can you massage the parameters of these curves to make them match as closely as possible?

### Weekly Challenge 44: Prime Counter

A weekly challenge concerning prime numbers.

### Weekly Challenge 28: the Right Volume

Can you rotate a curve to make a volume of 1?

# Weekly Challenge 24: Suspicious Integrator

##### Stage: 5 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.