3. Let f(z) be an analytic function in D = B₁(0) = {x² + y² < 1} and f(z)| = 1. Show that f(2)= C. Hint: differentiate the equation u² + v² = 1 with respect to x and y respectively, and then use Cauchy-Riemann equation.

Suppose that f(a) = f(b) = 0 and the second derivatives of f exist on the closed interval [a, b]. Prove that

2. Consider the function f: R²R such that f(x, y) = x²y-2xy² +6xy-3y² +18y +4. (a) Show that f has precisely two stationary points: (-4,-1), and (0,3). (b) Determine the nature of these two stationary points.

Determine whether the functions y₁ and y₂ are linearly dependent on the interval (0,1). y₁ = tan ²t-sec c²t₁ y₂ = 6 Select the correct choice below and, if necessary, fill in the answer box within your choice. © A. Since y₁ = (y₂ on (0,1), the functions are linearly independent on (0,1). (Simplify your answer.) B. 1 Y₂ on (0,1), the functions are linearly dependent on (0,1). Since y₁ = (Simplify your answer.) C. Since y₁ is not a constant multiple of y₂ on (0,1), the functions are linearly independent on (0,1). D. Since y₁ is not a constant multiple of y₂ on (0,1), the functions are linearly dependent on (0,1).