calculus

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

  • calculus -

    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)

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