Please answer the following questions and provide the work for it!

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Help Q 2 0 @ Q search Question 2 (21 points) [ kx + 2ky - y+2kz-z-2k=0 Given : 2/x + 3ky - y + 3kz -z-3k =0 (k is a constant) kx + 2ky-y+3kz-z-3k = 0 a. Find the values of "k" for which the system has: 1. A unique solution. 2. Infinitely many solutions. 3. No solution. b. Is there a value of the constant & for which the system would be homogenous? Explain. c. Plug k = 0 : 1. Find the solutions for the system. 2. Is there a solution for the system where x = y= z? If so, find it, and if not, explain why. 1628ULXGILL Question 3 (30 points) (there is no connection between the segments) a. Given the surface: z = f (x, y) = In x+1-5In(xy)? where x>e,y>0. A curve is created by the intercept of the surface with the plane z = 0. Find y' = ay dx at the point where y = 1. b. Find the limit lim ex - 2x-1 xvx C. Given the function: g(x, y) =x +y-xy. 1. Find all critical points for the function. 2. Choose one of the critical points and categorize it as max/min/saddle. Question 4 (25 points) Given the function: J (x ) = ( ex - 4 ) (ex - 1 ) a. Find the domain of the function. Explain your calculations. b. Find horizontal asymptotes (if any) using the appropriate limits. JUL 28 FAMEUND