1
Use Newton's Method with 5 iterations
-0.900000000000000
-0.892052469135802
-0.892003706245178
-0.892003704415253
-0.892003704415253
2
Find when
Error in lines 3-3
Traceback (most recent call last):
File "/projects/sage/sage-6.10/local/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 905, in execute
exec compile(block+'\n', '', 'single') in namespace, locals
File "", line 1, in <module>
File "/projects/sage/sage-6.10/local/lib/python2.7/site-packages/sage/calculus/functional.py", line 130, in derivative
return f.derivative(*args, **kwds)
File "sage/symbolic/expression.pyx", line 3765, in sage.symbolic.expression.Expression.derivative (/projects/sage/sage-6.10/src/build/cythonized/sage/symbolic/expression.cpp:22854)
return multi_derivative(self, args)
File "sage/misc/derivative.pyx", line 222, in sage.misc.derivative.multi_derivative (/projects/sage/sage-6.10/src/build/cythonized/sage/misc/derivative.c:2861)
F = F._derivative(arg)
File "sage/symbolic/expression.pyx", line 3833, in sage.symbolic.expression.Expression._derivative (/projects/sage/sage-6.10/src/build/cythonized/sage/symbolic/expression.cpp:23333)
raise TypeError("argument symb must be a symbol")
TypeError: argument symb must be a symbol
3
Suppose that x, y, and z are all functions of t, and
[D[0](z)(t) == -1/2*((2*y(t)*z(t) - 1)*D[0](x)(t) + (2*x(t)*z(t) - 1)*D[0](y)(t))/(x(t)*y(t))]
[]
[D[0](y)(t) == -(2*x(t)*y(t)*D[0](z)(t) + (2*y(t)*z(t) - 1)*D[0](x)(t))/(2*x(t)*z(t) - 1)]
[]
[D[0](x)(t) == -(2*x(t)*y(t)*D[0](z)(t) + (2*x(t)*z(t) - 1)*D[0](y)(t))/(2*y(t)*z(t) - 1)]
[]