Question 1. (a) Let f R² R defined by
f(r,y) = 0, (=g)² if =
Use E - 8 methods to prove continuity of the partial derivatives of f. Create an argument,
to show that f is differentiable at (0,0).
(b) Let f : R2 R defined by
f(x.y) = = (x,y) (0,0);
0. if =
Create an argument, using sequence methods, to investigate the differentiability of f at
(0,0). Discuss the differentiability of f at (z.y) + (0.0).
(c) Solve for the equation of the tangent plane to the graph of z = 00(2+++y) at (0.0).
(d) Solve for the equation of the tangent plane to the graph of z = 3x³ + 4y2 at (3.-1). -
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