Solve bx + c = 0 for x by means of the quadratic formula.
Applying the quadratic formula directly gives
(b +/ sqrt(b^2  4ac)) /(2a)
which is invalid or indeterminate due to division by zero.
But as a approaches 0 the limit can be found using l'Hopital's rule.
We have
b +/ (b^2  4ac)^(1/2)
2a
The derivative of the numerator with regard to a is
+/ 2c(b^2  4ac)^(1/2)
while that of the denominator is 2.
the result is then +/ c/sqrt(b^2) = +/ c/b.
How to tell which to use (+/) is a problem with this method.

Posted by Charlie
on 20071023 14:54:06 