Posted by Mario on Monday, February 16, 2009 at 3:04pm.
e^x and e^2x
x = 0, e^0 = 1 e^2*0 = 1
x = 1, e^1 = 2.72, e^2 = 7.39
x = 2, e^2 = 2.72, e^4 = 54.6
x = 3, e^3 = 20.1, e^6 = 403
etc (diverge fast from each other)
ln x and ln 2x
do not try ln 0
x = 1 , ln 1 = 0, ln 2 = .693
x = 2 , ln 2 = .692 , ln 4 = 1.39
x = 3 , ln 3 = 1.1 , ln 6 = 1.79
(do not diverge from each other so fast)
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x = 10 , ln 10 = 2.30 , ln 20 = 3.00