Homework Statement
Let f(x,y) = xe^{x^2 + y^2} + y^3 + cos x
a) Show there exists a differentiable function \phi(y) such that x = \phi(y) solves f(x,y) = 1 in some neighborhood of (0,0) in R^2. (Meaning (x,y) satisfies f(x,y) = 1 for (x,y) near (0,0) if and only if x = \phi(y)) Prove your...