Alexandria L.

asked • 01/14/15

Approximation to lnx

A good approximation to lnx is given by

(((3A2)/(5)+1)*(A2)/(3)+1)*2A

Where A=(x-1)/(x+1) and 1/2≤x≤3/2
Use this formula to calculate ln1.4

Mark M.

The plethora of parenthesis has me puzzled.
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01/14/15

Fartash Y.

i don't exactly know what is your expression because of the parenthesis,however i can tell that in this expression A is a numerator which means if you find the A's minimum and you put it in the expression you find the expression's minimum,you can apply this for the maximum too. so i' m gonna find the min and the max of A then you just have to put them in the expression.here's the solution:
 
0.5<x<1.5 => -0.5<x-1<0.5 •, 1.5<x+1<2.5 =>  1/1.5<1/(x+1)<1/2.5 ••
 
•,•• => -0.5/1.5<(x-1)/(x+1)<0.5/2.5 =>  -1/3<A<0.2  => min{A}=-1/3  ,   max{A}=0.2
 
 
 
 
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01/18/15

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