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ThePerfectHacker · #2 November 4th, 2007, 12:48 PM

Quote:

Originally Posted by Paige05

I have 3 questions that I'm stuck on.. if you have any idea about any of them please help me out!

Thanks!

1. Use the fact that ln x and e^x are inverse functions to show that the inequalities e^x >/= 1+x and ln x </= x-1 are equivalent for x>0.

$e^x \geq 1+x$ is equivalent to saying $e^x - x - 1 \geq 0$ so let $f(x) = e^x - x - 1$ on $(0,\infty)$ since $f'(x) = e^x - 1$ and $f'(x)>0$ it means the function is increasing.