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Problem 1 let f ( x , y, = ) = x 8 + xy z t x2 2 9) Find the directional derivative of fix,yiz ) in the direction of u = (i - j - k ) / 53 at point (1, 1, 1 ) . b) If the independent variables were constrained such that x y + yz + x z = 3 , find ( Jz )x of ) at ( 1, 1,1 ). [ Hint : consider ushe implicit differentiation ]. () suppose that f(x,y, 2) represents the temperature distribution in three dimensions, A particle initially located at ( 1,1,1 ) moves by 0-02 units in the x directions, - 0.01 units in the y-directive, and 0.03 units in the 2-direction. what is the approximat change in the observed temperature ? starting at point (1ilil) at particle travels along the bath r (t ) = ti +;+ ( 26 - 1 )K. What is the value of of at t = 1 ? df by the