x*x*cos(1/x)

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Solution for x*x*cos(1/x) equation: 


D( x )

x = 0

x = 0

x = 0

x in (-oo:0) U (0:+oo)

x*x*cos(1/x) = 0

x*x = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

cos(1/x) = 0

cos(1/x) = 0  <=>  1/x = pi*k_1+pi/2 i k_1 należy do I

t_1 = pi*k_1+pi/2

1/x-t_1 = 0

1*x^-1 = t_1 // : 1

x^-1 = t_1

-1 < 0

1/(x^1) = t_1 // * x^1

1 = t_1*x^1 // : t_1

1/t_1 = x^1

x = 1/t_1

x = 1/pi*k_1+pi/2 i k_1 należy do I

x*x*cos(1/x) = 0  <=>  x*x = 0 or x*x*cos(1/x) = 0  <=>  cos(1/x) = 0

x in { 0} 

x = 1/pi*k_1+pi/2

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