The answers correspond to the problem number on the “Questions” page.
1) dr/dt=.001243 cm³/sec
2) If the width of the window is w, then the equation for area, A, of a square is A = w². If the error in measurement value of w is denoted by dw = Δw, then the corresponding error in the calculated value of A is ΔA, which can be approximated by the differential
dA = 2wdw
When w = 80 and dw = 1, this becomes
dA = 2(80)1 = 160
The maximum error in the calculated area is 160cm².
3)a) Absolute minimum at x=1
b) The function is decreasing on the interval (-∞, –√3) and (√3, ∞). The function is increasing on the interval (-√3, √3)
c) Absolute maximum at x= 3^(-3/2)