H V X C GQE 1 / 1 250% + does not have a tangent plane at the point (0, 0), while the function h(x, y) = (x2 +2) e-x2-y has a tangent plane at this point. Problem 3. Consider the function f (2, y ) 20 4 + 2 / 2 (2, y) # (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 ) = (202 + y2 ) e - 202 - 32. A particle is moving along the hyperbola x2 - y2 =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). ") Calmulate the rate of change of the dencity of the narticle at the time + chained in nort () 1 7.C 8:26 PM Mostly cloudy Q Search ENG US 2023-09-20