-- Exercise 2.5
-- George C. Privon
-- 2023-09-05

-- a) cube root of x
cuberoot :: Double -> Double
cuberoot x = x ** (1/3)

-- b) e^y + 8^y
exp8 :: Double -> Double
exp8 x = exp x + 8**x

-- c) 1/sqrt((x-5)^2 + 16)
h :: Double -> Double
h x = 1 / (sqrt $ (x-5)^2 + 16)

-- d) 1 / sqrt(1-beta^2)
gamma :: Double -> Double
gamma x = 1 / (sqrt $ 1 - x^2)

-- e)  1/(10+x) + 1 / (10-x)
bigU :: Double -> Double
bigU x = 1 / (10 + x) + 1 / (10-x)

-- f) sqrt(l*(l+1)
bigL :: Double -> Double
bigL x = sqrt $ x * (x + x)

-- g) 1 / abs(x)^3
bigE :: Double -> Double
bigE x = 1 / (abs x)^3

-- h) 1/ (x^2 + 4)^3/2
bigE2 :: Double -> Double
bigE2 x = 1 / (x^2 + 4) ** 1.5