Instructions With this background, here's your assignment: *You must show sufficient detail to support your work to earn credit for your calculations. This can be hand-written work, typed calculations, or excel formulas. To avoid round-off error, retain at least six decimal places in all of your calculations. Complete all trigonometric calculations in radians. . Assume the function f is defined as f (x, y) = 2 sin atany . Use differentiation rules to find the exact partial derivatives a ar of and dy Of, and evaluate those exact partial derivatives at (-3.1, 1.56). . Use the finite difference formulas to estimate of of and - dy of at (-3.1, 1.56). . for three different values of the mesh size o h = 0.01 o h = 0.001 o h = 0.0001 . Use your calculated values to fill in this table: Estimated partial derivatives using finite difference formulas: finite difference finite difference h of approx. to of exact- fe approx. to of exact - dy 0.01 0.001 0.0001 Answer the following questions: . For which partial derivative ( or (of or dy of ) is the finite difference approximation consistently more accurate? . Why is the finite difference approximation for the other partial derivative is consistently less accurate? (Hint: What happens to the tan y function near y = 1.56?). . Share a real-world example that might cause similarly poor approximations using this method. Upload your results using the submission instructions found below. If your submission contains multiple pages, please upload one file with multiple pages (as a pdf or doc, or xIs). You may handwrite or type your submission. If you use Excel, upload the Excel file so that the formulas can be viewed. If you use Mathcad, do not submit a Mathcad file, but instead submit a pdf or doc file with images of your work