Question 1040748
(i) {{{y = sqrt(5x+4)}}} ==> {{{dy/dx = 5/(2sqrt(5x+4))}}} ==>  {{{dy(1)/dx = 5/(2sqrt(5*1+4)) = 5/(2*3) = 5/6}}}


(ii){{{y = sqrt(5x+4)}}} ==> {{{dy/dt = (5*(dx/dt))/(2sqrt(5x+4))}}}  ==>  {{{dy(x=1)/dt = (5*0.03)/(2sqrt(5*1+4)) = 0.075/3 = 0.025}}} unit per second.


(iii) Area = {{{int(sqrt(5x+4), dx, -4/5,1)}}}

=  {{{(1/5)int(sqrt(5x+4), d(5x+4), -4/5,1)}}}

= {{{(1/5)(2/3)((5x+4)^(3/2))^1[-4/5]}}}

= {{{(2/15)(9^(3/2) - 0^(3/2)) = (2/15)*27 = 18/5}}}