1) if dy/dx = x√x^2-4, and y=2 when x=√5, find y in terms of x.
(use the substitution u = x^2 - 4)
2) if f`(x) = 3x/√(x^2+1) for all x, find f(x) given that f(0) = 2.
(use the substitution u=x^2+1)
3) if dx/dt = t-1/√(t^2 - 2t + 4) and x = 10 when t =0,
find x in terms of t. (use the substitution u = t^2 -2t+4)
4) find the equation of the curve whose gradient at any point
x>1/2 is √2x -1 and which contains the point (5/2, 9).
(use the substitution u = 2x -1)
(use the substitution u = x^2 - 4)
2) if f`(x) = 3x/√(x^2+1) for all x, find f(x) given that f(0) = 2.
(use the substitution u=x^2+1)
3) if dx/dt = t-1/√(t^2 - 2t + 4) and x = 10 when t =0,
find x in terms of t. (use the substitution u = t^2 -2t+4)
4) find the equation of the curve whose gradient at any point
x>1/2 is √2x -1 and which contains the point (5/2, 9).
(use the substitution u = 2x -1)
