1. Consider the following statements about the surface equation z = ye-* - 2xy and the point P(0, -2) in your domain: I. If we calculate the directional derivative of z in the direction of any vector @ e R-, it is certain that Do z (P) = v37. II. There is no direction from P such that the directional derivative of z computed in that direction yields 1. III. The value of the directional derivative of z at point P calculated in the direction of the vector u = (3, 4) is equal to -14. Which of the above statements are TRUE: A) Only I and III. B) None. C) Only the I. D) Only II.10. Consider the region R shown in the following figure, which involves the curves of equations x ~ + y= = 9, + 49- 9 : 1 R 7 -3 The double integrals that allow us to calculate the area of the region R correspond to 49 (1-15) 49 (1-4) dady + drdy 49 (1-42) 49 (1-42) dady + dedy 9-ya 91- dydx D) dydex 11. Consider the curve C of equation x2 + y? = (x3 -2x + y")3. Among the indicated options, select the one that correctly shows a possible equation for C in polar coordinates and the equation of a line tangent to the pole. 9/1 = g ajod ay1 0 queBuen yum '(9)uIs - 1 = J:5 (v B) Cor =1+ 2 sin(0), with tangent to the pole 0 = 7n/6 C) Car = 1+ 2 cos(0), with tangent to the pole 0 = 2n/3 D) C:r=1+ 2 cos(0), with tangent to the pole 0 = 1/32. Let f be a function that admits continuous second partial derivatives such that Vf(x, y) = (alx - alx], y= + ay) with a