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Newton's Method question?
Find all roots of the equation ln(4-x^2)=x correct to 8 decimal places. List all successive approximations.
I chose x=1 for my first guess and I ended up getting 1.22462048 after 6 times i pressed enter on my calculator
But I looked at the graph and there appears to be another root at x=-1.8 (approximately) but when I plugged near by numbers like -2 and -1.5 I ended up getting some answer for each and after I pressed enter for the second time on my calculator it says DOMAIN ERROR....=(
What am I doing wrong?!?
2 Answers
- ted sLv 78 years agoFavorite Answer
nothing...Newton's method conditions are not met in a neighborhood of ( - 2 ) ...
the zero is ≈ [ - 1.96478 ]......too close to the boundary of ln ( 4 - x² ) , x in ( -2 , 2 )
- ?Lv 68 years ago
It's really close to x=-2 where the function you are using is no longer defined. What's happening is that Newton's method is shooting you out past that point and trying to take a log of a negative number.
