Sqrt(4-x^2)

Sqrt(4-x^2)

Input
sqrt(4 – x^2)
Alternate form
sqrt(2 – x) sqrt(x + 2)
Series expansion at x=-2
2 sqrt(x + 2) – 1/4 (x + 2)^(3/2) – 1/64 (x + 2)^(5/2) + O((x + 2)^(7/2))
(Puiseux series)
Series expansion at x=0
2 – x^2/4 – x^4/64 + O(x^5)
(Taylor series)
Series expansion at x=2
2 sqrt(2 – x) + 1/4 sqrt(2 – x) (x – 2) – 1/64 sqrt(2 – x) (x – 2)^2 + 1/512 sqrt(2 – x) (x – 2)^3 – (5 sqrt(2 – x) (x – 2)^4)/16384 + O((x – 2)^5)
(generalized Puiseux series)
Series expansion at x=∞
sqrt(-x^2) – (2 sqrt(-x^2))/x^2 + O((1/x)^4)
(Puiseux series)
Derivative
d/dx(sqrt(4 – x^2)) = -x/sqrt(4 – x^2)
Indefinite integral
integral sqrt(4 – x^2) dx = 1/2 sqrt(4 – x^2) x + 2 sin^(-1)(x/2) + constant
Global maximum
max{sqrt(4 – x^2)} = 2 at x = 0

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