0 < x < 2. Let f(x) eCos T sin a < x < 27 2 Let g(æ) = f(s)ds = Ss T Find g and g(27). 2

as a #1 Assume that Z= z (xy) is implicitly determined as function of x, y by the equation √3-1 sin(x-y)+sin(y-3)+sin(z-x)== (a) Find E and Iz 825 (6) Evaluate ez 8x ду 2 and az at the ㅠㅠㅠ |point (x, y, z) = (TT - 316 (c) Find the equation of the tangent plate to the given surface at ㅠㅠ ㅠ the point (+1+1=7). (苦) 6 6

For each function given below in (i)-(iii), perform the following steps in Mathematica (do not forget to comment/text your steps). (i) f(x, y) = x sin (2y) + y sin 2x (ii) f(x, y) = (sin x)(cos y)e-√²+y²/8 (iii) f(x, y) = y² + y³ – x³ (a) Plot the surface z = f(x, y) (you can use either ContourPlot3D or Plot3D, make sure to use the proper parameters in either case, use "Help"). Choose appropriate range for the variables so that the graph features are clearly seen in the figure. (b) Plot several level curves of f(x, y) using Contour Plot.

Exercise 11. For what values of p is the function f(x) = { x² sin (1) x #0 x = 0 0 differentiable?

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