1. (6pts)Draw the graph of a single function with the following properties: f (1) =1, lim f(x) =5, lim f(x) =3, lim f(x) =4, f(3) =4, lim f(x) =2 X-+3- * - 3 + 2. (6pts) Sketch a graph of the derivative of the following function on separate axes 3. (12 pts) Demonstrate how to evaluate the following limits: lim 4x + 3x5 +4x x *+ 2x +1 lim sin 7x x-0 sin 6x 4. (6pts) Demonstrate how to evaluate the derivative f'(2) using the definition of the derivative i.e. (S ( a ) = lim f(ath ) - f ( a ) h -+ 0 h or f'( a ) = lim f (x) - f(a) for the function f (x) = x4 x -a 5. (6pts) What value for k, will make the following function be continuous for all real numbers? Show the limit exists by using left and right-hand limits. f (x ) = x +3 x54 kx - 3 x> 4 6. (6pts)Show all steps in deriving dx gay below (including writing the function with correct exponents)