3cos2x
Input |
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3 cos(2 x) |
Roots |
x = (pi n)/2 – pi/4, n element Z |
Series expansion at x=0 |
3 – 6 x^2 + 2 x^4 + O(x^6) (Taylor series) |
Derivative |
d/dx(3 cos(2 x)) = -6 sin(2 x) |
Indefinite integral |
integral 3 cos(2 x) dx = 3 sin(x) cos(x) + constant |
Global maxima |
max{3 cos(2 x)} = 3 at x = pi n for integer n |
Definite integral |
integral_0^(pi/4) 3 cos(2 x) dx = 3/2 = 1.5 |
Definite integral mean square |
integral_0^pi (9 cos^2(2 x))/pi dx = 9/2 = 4.5 |