6. (10 points) Find all asymptotes of y = 2x3 + 2x + 1 x2 - 5r + 6 7. (10 points) Two runners start a race at the same time and finish in a tie. Prove that at some time during the race they have the same speed. Hint: Try to make a connection between this problem, and one of the important theorems you learned in this course! When you want to use the relevant theorem, make sure that you will explicitly check all the conditions of the theorem. 8. (10 points) Using the Mean Value Theorem, prove that v1 + x2 0. Make sure to check all the necessary conditions of the Mean Value Theorem! 9. (10 points) Using the Riemann sum definition of integrals, find lim n2 + j=1 10. (10 points) Let f(x) = vx and g(x) = x2. (a) Sketch graphs of f and g, and indicate the finite region enclosed by the graphs of these two functions. (b) Find the area of the region in part (a). 3x 2 - 1 11. (10 points) Let F(x) = 12 dt. Using the Fundamental Theorem of Calculus, find F(x) (i.e. the derivative of F(r) with respect to r). What is F'(1)