write a simplified algebraic expression in terms of a and h to estimate the instantaneous rate of change of 8t(t+2)

Answer 1

rate=changeinfunction/deltat as deltat >>0

rate=(8(t+h)(t+h+2))/h - 8(t(t+2)/h=
= 8/h * [(t^2+th+2t+ht+h^2+2h)-t^2+2t)
= 8/h * ( +2th+ +2h)
= 8 (2t+2)= 16(t+1)
and at t=a, then
ratechange=16(a+1)