9514 1404 393
Answer:
Step-by-step explanation:
(a) Solving the x-equation for u gives ...
u = (x -1)/4
Differentiating both equations with respect to u, we have ...
dy/du = 1 -4u
dx/du = 4
Then dy/dx is ...
dy/dx = (dy/du)/(dx/du) = (1 -4u)/4
Substituting for u gives ...
dy/dx = (1 -4(x -1)/4)/4
dy/dx = (2 -x)/4
__
(b) The approximate change in y is ...
∆y ≈ (dy/dx)(∆x)
For ∆x = 2.98 -3.00 = -0.02, and x=3, the approximate change is ...
∆y ≈ (2 -3)/4(-0.02)
∆y ≈ 0.005
