1) Prove : 1 x x²
1 y y²
1 z z²
= (x - y)( y - z)(z - x).
2) For the function f(x)= 2x³ - 24x + 5, find
a) the intervals where it is increasing.
b) the interval where it is decreasing.
3) Evaluate : dx/(5+ 2cosx) at (π, 0).
4) Evaluate : ∫ √tanx dx.
5) Find the value ¹₀∫(2x²+ 5x).
6) The two lines of regression for a biveriate distribution (x,y) are 3x + 2y = 7 and x + 4y =9. Find the regression coefficients bᵧₓ and bₓᵧ.
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