I need solve this assignment

Work Problem (60 points) You must provide a clear and detailed solution step by step for each question. Question 1 [20 pts] Let C be a curve defined by the vector equation r(t)= . a) [08 pts] Show that the point P (32, 52, e32 ) lies on the curve C. b) [12 pts] Find parametric equations for the tangent line to the curve C at the point P. Question 2 [20 pts] Given the function of two variables f (x, y) = -(x - 7)2 In (y + 2)-(2x+7y). a) [12 pts] Find all the first partial derivatives of the function f(x, y). b) [08 pts] Determine the point(s) where the following function is defined g(x, y) = V-(x - 7) In (y + 2)-4x2 - 28xy - 49y2. Question 3 [20 pts] Find the limit, if it exists, or show that the limit does not exist. a) [10 pts] lim 7x2 +2y (x, y)-(0,0) 2y b) [10 pts] lim 49x2-98xy+49 y2 (x, y)-(0,0) 7x-7y