Please solve 1-5 and show work on paper clearly, thanks!

1. (10 points) Find the horizontal asymptote. f (x ) = 2x + 30sin?(x) (x) f (x) = 3x - V9x2 - 2x +2 2.) (15 Points) Find the height and the radius of the least expensive closed cylinder which has a volume of 1000 cubic inches. Assume that the material cost is free, but the welding cost $0.80 per inch, to weld the top and bottom onto the cylinder and to and join the side as per the figure on the right. welding Fig. 5 3. (15 Points) Consider a symmetric cross inscribed in a circle of radius R=5 ft. Write the dimension of the cross that maximizes its area. You can use a software to faster any algebra simplification when showing your step-by-step solution. .2R 4. (10 Points) The function f (x) = e 2b defines the Gaussian distribution used extensively in statistics and probability; its graph is a "bellshaped" curve (see the graph). -( x-c) Gaussian (a) Show that f has a maximum at x = c. (The value c is called the mean of this Distribution f(x) = - distribution.) (b) Show that f has inflection points where x = c + b and x = c - b. (The value b is called the standard deviation of this distribution.) c- b c+b 5. (20 Points) Evaluate the limit: lim (ex Vx) lim (sin(x))x lim 1 x-1+ In (x) X - 1) lim ( 1 + 5) *