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A: compare this equation with here we have
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- Determine if f(x,y) continuous at (0,0). = 5x6y2 (x4+y²)² 0 if (x, y) = (0,0) if (x, y) = (0,0) isII. Determine whether or not the function x² + 2y if (x, y) + (0,0) f (x, y) = 1 et-y 2 if (x, y) = (0,0) is continuous at (0, 0). If discontinuous, identify the type of discontinuity.S (x, y)= I+x* + y? 1-x² - y² 2. Determine the points at which the function is continuous.
- Consider the function 2yx+3x T²+3y² 0 Determine whether this function is continuous at (0,0). F(x, y) = if (x, y) = (0,0) if (x, y) = (0,0)Find the linear approximation to the function f(x, y) = sin y --- |T at x, = (1, -2) 2 and use it to approximate f(1.02, -1.97) without a calculator.Determine whether the function xy²/³ + xy x⁹ + 2y³¹ h(x, y) if (x, y) = (0,0) if (x, y) = (0,0) √3 is continuous at the point (0,0) or not. If not, determine whether the discon- tinuity is removable or essential.
- Show that the function g(x, y) = is not continuous at (0,0). xy 2x² + y²¹ 0, (x, y) ‡ (0, 0) (x, y) = (0,0)Determine the analytic function f (z) = u + iv, if u - v = COS x + sin x –e¯y and f(t/2) = 0 2(cos x - cosh y)Let f (x, y) and g(x, y) be functions of two variables withthe property that ∂ f/∂x= ∂g/∂x and ∂ f/∂y= ∂g/∂y for every point(x, y) ∈ R2. What is the relationship between f and g?