Consider the equation sin(xyz) + x + y^2 + z^3 = 0. (a) Is there a differentiabl
ID: 2895072 • Letter: C
Question
Consider the equation sin(xyz) + x + y^2 + z^3 = 0. (a) Is there a differentiable function f such that x = f(y, z) solves the equation near (0, 0, 0)? If so, find partial differential0_y f(0, 0) and _z f(0, 0). (b) Is there a differentiable function g such that y = f(x, z) solves the equation near (0, 0, 0)? If so, find partial differential_x g (0, 0) and partial differential_z g (0, 0). (c) Is there a differentiable function h such that z = h(x, y) solves the equation near (0, 0, 0)? If so, find partial differential_x h (0, 0) and partial differential_y h (0, 0).Explanation / Answer
The answer for all three is no.
Because you can't find f(x,y) ,f(x,z) and h(x,y)
Because there is combination of x and sinx, y and siny , z and sinz Hance you can't take x ,y ,z common and find the relative function