Homework Sourse1a If x 2t ln2t and y t2 lnt2 where t0 find the value of
1a. If x = 2t - ln(2t) and y = t^2 - ln(t^2) where t>0, find the value of t at the point on the curve at which the gradient is 2.
1b. Determine the finite area enclosed by the curves y^2 = 3x and x^2 = 3y.
NB: please go through the solution step by step as im having hard time to grasp the concept, thanks in advance!
1b. Determine the finite area enclosed by the curves y^2 = 3x and x^2 = 3y.
NB: please go through the solution step by step as im having hard time to grasp the concept, thanks in advance!
Solution
1a. x = 2t - ln(2t) dx = 2 - 2/2t = 2 - 1/t y = t^2 - ln(t^2) dy = 2t - 2t/t^2 = 2t - 2/t dy/dx = 2 or, (2t - 2/t)/(2-1/t) = 2 or, 2t-2/t = 4-2/t 2t = 4 t = 1/2
