Consider the function given as example in lecture: f(x, y) = (e
x cos(y), ex sin(y)) (6.2) Denote a = (0, π/3) and b = f(a). Let f
−1 be a continuous inverse of f defined in a neighborhood of b.
Find an explicit formula for f −1 and compute Df−1 (b). Compare
this with the derivative formula given by the Inverse Function
Theorem.
Find the linearization
at x=a.
f(x)=sin^7(x),
a=π/4,
(Use symbolic notation
and fractions where needed.)
Find the linearization
of y=e^(√7x) at x=36.
(Use symbolic notation
and fractions where needed.)