Further Exercises 7.4 . The Earth is round. but in everyday life, we get along ne acting as though it were flat. Why is this possible? . Compute the following partial derivatives: f l. f(X. Y) = X3 Y3 +2XY. Compute :7 2 3 Bu 2. u(s, t) = 5s 3st + 6t +8. Compute g. 6 3. r(N. P) = 3P(1+ NP) + Iog(3N) + .2\". Compute 52' . Compute both partial derivatives of 1"(X, Y) = 5X2 + 2Y3 4X3Y5. _ _ _ 2 2 Y23 . Compute all three partial derivatives of 9(X. Y, Z) = (X Y )(4X + 22) e X + 23 . . Compute the Jacobian matrix of the function g{u, v) = (U2 + v3 + 2. E) . Let f(X. Y) = 5XY 3X2 - Y2. 1. Compute both partial derivatives of f. 63' 6f 2. Compute a [12) and W from part (a). _ That is, plug (X,Y) = (1,2) into your answer (1-2) 3. Write down the linear approximation to f(X, Y) at (X, Y) z (1.2) in the form fm-AX+n-AY 4. Expand your answer from part (c) by rewriting Af as 1"(X, Y) f(1. 2) and replacing AX and A'/ as in problem 1 above, then solving for f(X, Y). 5. What is {(0912.06) approximately? 6. Use your answer from part (d) to write down the equation for the tangent plane to the graph of f(X,Y) at (X,Y) = (1.2)