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taylor polynomial of sin(x) at x=0
taylor polynomial of log(x) at x=1
taylor polynomial of log(1+x) at x=0
taylor polynomial of exp(x) at x=0
taylor polynomial of exp(-2*x) at x=0

1+1/2+1/3+1/4+...
1+x+x^2+x^3+...

fourier series expand
function:  Piecewise[ { {-1, -pi < x < 0}, {1, 0 < x < pi} } ]
variable:  x
oreder:    10

grad ( 6*x/(2+x^2+y^2) )
plot z = 6*x/(2+x^2+y^2), -6 <= x <= 6, -5 <= y <= 5
min z = 6*x/(2+x^2+y^2), -6 <= x <= 6, -5 <= y <= 5
max z = 6*x/(2+x^2+y^2), -6 <= x <= 6, -5 <= y <= 5

plot z = sin(x)*sin(y), -PI*3/2 <= x <= PI*3/2, -PI*3/2 <= y <= PI*3/2
saddle points of z = sin(x)*sin(y)

taylor polynomial of log(1+x^2) at x=0
1-1/2+1/3-1/4+...

plot x^2+y^2, -5 < x < 5, -5 < y < 5
plot x*y, -5 < x < 5, -5 < y < 5 

 ALTRO