X + V X E 1 / 1 | - 253% f (x , y ) = 20 4 + 2 2 (2, y) # (0, 0) 0 (x, y) = (0, 0) Show that this function has directional derivatives in all directions at the point (0, 0) and, consequently, possesses partial derivatives. However, demonstrate that the function is not continuous at (0, 0), leading to the conclusion that it is not differentiable at this point. Problem 4. The mass density function of a substance is given by: p ( 20 , y ) = (2 2 + 2 ) e - 202 - 2 A particle is moving along the hyperbola x2 - y' =1 with the parametric function y(t) = (cosh(t), sinh(t) ) for te (-1, 1) a) Determine the time t when the density of the particle is maximized. b) Find the tangent vector to the path of the particle at the time t determined in part (a). c) Calculate the rate of change of the density of the particle at the time t obtained in part (a). Problem 5. A runner is following the path of a hyperbola given by y = (cosh(at), sinh(at)) in a field with a temperature distribution represented by T(x, y) =30e- -y. Let's assume that the runner is wearing a wristwatch with markings ranging from T=0 to T=30. Find the angular velocity function of the watch's hand in torme of w Create a not denisting the anmilar volocity as a function of time for a -1 2 within the time GBP/CAD Q Search ENG 1:14 PM 0.33% D US 2023-09-20 1