Instructions: Show all your work for full credit. Indicate your answers clearly. Problem 1. (13 pts each) Evaluate each of the following limits. (2) lim - w2 + w - 2 (22) lim V3 - y - V3 (izi) lim ~ - VX -+ 1 w2 + 4w - 5 a - 1 For (iii), you may, without proof, use the following fact: a3 - 63 = (a - b)(a2 + ab + 62), for any real numbers a and b. Problem 2. (12 pts) Find the vertical and horizontal asymptotes of the function h(x ) = : x - 5x2 3x2 + 2x Problem 3. (13 pts) Find the constant a that makes the function g continuous everywhere on R. 9 (20 ) = Jax2 +5x, if x 2. Is F differentiable at x = 2? Explain why or why not. Problem 5. (13 pts) Determine the equation of the tangent line to the curve f (t) = t2 + 4t - 1 at the point t = 1. Problem 6. (10 pts) Provide an example of a function defined everywhere on R that is not differentiable at exactly two points. Justify your