Steve, you've been an amazing help. Thank you so much. This is the last question I need checked.

Solve ∜82 using differentials. I got 3.00926

y = x^(1/4)

dy = 1/4 x^(-3/4) dx
y(81) = 3
dx=1, so dy = 1/4 * 1/27 = 1/108

y(82) ≈ 3+1/108 = 3.00926