1. Consider the equation ze + sin(ry) + y - In(2)-0. Find the value of dy/dr...

 

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1. Consider the equation ze + sin(ry) + y - In(2)-0. Find the value of dy/dr at the point (0, in 2). 2. Consider the equation sin(x + y) + sin(x+2)+ sin(y+ 2) = 0. Find the values of 8z/0x and Oz/0y at the point (,,). 13 3. Let f(x,y) (x+2)/2 and T be the triangular region cut from the first quadrant by the line 2+ y = 1. Let u (u,u2) be a unit vector. Find the average value of Duf over the region T. 4. A flat plate has the shape of the region x+y2 <1. The plate is heated and the temperature at the point (x,y) is given by T(x,y) = x+2y2-r. Find the temperatures at the hottest and coldest points on the plate. 1. Consider the equation ze + sin(ry) + y - In(2)-0. Find the value of dy/dr at the point (0, in 2). 2. Consider the equation sin(x + y) + sin(x+2)+ sin(y+ 2) = 0. Find the values of 8z/0x and Oz/0y at the point (,,). 13 3. Let f(x,y) (x+2)/2 and T be the triangular region cut from the first quadrant by the line 2+ y = 1. Let u (u,u2) be a unit vector. Find the average value of Duf over the region T. 4. A flat plate has the shape of the region x+y2 <1. The plate is heated and the temperature at the point (x,y) is given by T(x,y) = x+2y2-r. Find the temperatures at the hottest and coldest points on the plate.