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Problems
In Problems 1-16, find the increment and total differential. In Problems 17-22, express Δz in the form Δz = dz + ε1 Δx + ε2 Δy. In Problems 23-40 find the tangent plane at the given point. 41 Show that if z is a linear function of x and y, z = ax + by + c, then Δz = dz at every point (x, y). 42 Let f(x,y) =
43 Let f(x, y) = . Prove that at the point (0,0),
44 Let f(x, y) = |xy|. Show that at (0,0),
45 Let f(x, y) = |x| + |y|. Show that at (0, 0),
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