 # Calculus Problems

## Transcribed Text

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); if # 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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