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Question 4 (2 marks) Attempt 1 A surface is described by the equation re10y+9y For a surface defined by a vector R(t,y)y,z(ry), the element of surface area is given by dS For the given surface, determine the cross product Each component should be expressed using the correct Maple syntax; for example, one component might be: -31+7'x exp(-11 y) The first component of the cross product is The second component of the cross product is The third component of the cross product is 1-(9cosh(s+v) 1t (dasalarcoshialfunctionf(xy,z) uchthatyg adfandt(0,02% 2 4x ch that I grad f and f(0,0,0)-0 expressed using the correct Maple syntax; for example: 4'y'sinh(x-z)+7'y'z+2x*2 The vector field I is conservative, find a scalar potential function f(x,y,z) su Do not use decimal approximations all numbers must be correct Maple expressions The scalar potential is f(x,y,z) = Evaluate the line integral: (132 I9r2 dx+(1022+6e cos(22) dy+(20yz-2e6Vsin(22) dz. 0,0,0) Your answer can be expressed as a number accurate to five significant figures or as an expression in correct Maple syntax. For example: exp(5/2)"cos(4*Pi)+5°(Pi^2)/3-1 OR 27.63 183464 OR rounded to 27.63183 Change the order of integration and evaluate the following double integral: 20 cos() d dy can be expressed as a number accurate to five significant figures or as an expression in correct Maple syntax For example: 70/(3 Pi sqrt(2) OR 5.251845176 OR rounded to 5.25185

Answer 1

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