We have an equation called (*) where e-x = x3 where we have that x is an element of R. Where the unique solution to (*) is called r. a) Use Newton’s method once with the starting value (x0= 1/2 ) to find an approximate value for (r). b) Then justify whether the approximate value found in part a is greater or less than (r), without using a calculator and without substituting the value into the equation (*).

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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We have an equation called (*) where e-x = x3 where we have that x is an element of R.

Where the unique solution to (*) is called r.

a) Use Newton’s method once with the starting value (x0= 1/2 ) to find an approximate value for (r).

b) Then justify whether the approximate value found in part a is greater or less than (r), without using a calculator and without substituting the value into the equation (*).

 

 
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