= is a so- 3. 14.3: Second Partial Derivatives: Verify that the function u(x, y, z)...

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= is a so- 3. 14.3: Second Partial Derivatives: Verify that the function u(x, y, z) = 0 everywhere, except of √x²+y²+z² lution of the three dimensional Laplace equation Uxx + Uyy + Uzz course at the origin where u is not defined. 4. 14.4, Tangent Planes and Linear Approximation: Let f(x,y)=√x² + y². (a) Calculate the equation of the tangent plane to the graph of f at (3,-4,5). (b) Use a linear approximation to find the approximate value of f(2.9, -4.1). 1 5. In this multiple choice problem provide a justification for your answer. The figure below shows level curves of the function f(x, y). The tangent plane approx- imation to f(x, y) at the point P = (xo, yo) is f(x, y) c+m(x-xo) + n(y-yo). What are the signs of c, m, and n? " (a) c> 0, m>0, n > 0 (b) c <0, m > 0, n < 0 (c) c> 0, m < 0, n > 0 (d) c <0, m < 0, n < 0 (e) c> 0, m> 0, n < 0 = is a so- 3. 14.3: Second Partial Derivatives: Verify that the function u(x, y, z) = 0 everywhere, except of √x²+y²+z² lution of the three dimensional Laplace equation Uxx + Uyy + Uzz course at the origin where u is not defined. 4. 14.4, Tangent Planes and Linear Approximation: Let f(x,y)=√x² + y². (a) Calculate the equation of the tangent plane to the graph of f at (3,-4,5). (b) Use a linear approximation to find the approximate value of f(2.9, -4.1). 1 5. In this multiple choice problem provide a justification for your answer. The figure below shows level curves of the function f(x, y). The tangent plane approx- imation to f(x, y) at the point P = (xo, yo) is f(x, y) c+m(x-xo) + n(y-yo). What are the signs of c, m, and n? " (a) c> 0, m>0, n > 0 (b) c <0, m > 0, n < 0 (c) c> 0, m < 0, n > 0 (d) c <0, m < 0, n < 0 (e) c> 0, m> 0, n < 0