- A The Temperature At A Point X Y Z Is Given By T X Y Z 300e X 3p 9 Where T Is Measured In C And X Y Z In 1 (41.74 KiB) Viewed 27 times
A) The temperature at a point (x, y, z) is given by T(x, y, z)= 300e-x-3p²-9₂² where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P(2, -1, 4) in the direction towards the point (5, -5, 5). *C/m az B) Use the Chain Rule to find the indicated partial derivatives. Əs (b) In which direction does the temperature increase fastest at P? дz at (c) Find the maximum rate of increase at P. az ди 9.(0, 0) 9.(0, 0) = 11 || z = x² + x²y, x = s + 2t - u, y = stu²; дz дz дz when s= 2, t = 1, u = 5 I as' at au Suppose f is a differentiable function of x and y, and g(u, v)-f(e" + sin(v), e" + cos(v)). Use the table of values to calculate 9, (0.0) and 9.(0,0). 7 9 fx ty 10 3 6 01 5 8 (0, 0) (1, 2) Find the directional derivative of f at the given point in the direction indicated by the angle 8. f(x, y) = y cos(xy), (0, 1), 0 = π/3