You must show your work for full credit. 1. (3 points) Consider an athlete running a 4-0-m dash. The position of the athlete is given 3 by function 5(t) = t; + 4t where s is the position in meters and t is the time elapsed, measured in seconds. Compute the average velocity of the runner over the given time intervals in part b. a. [2.9953005] 30(2) 30(1) _ 38.005) s(2.995) x2 x1 3.005 2.995 msec = _ 16.542538 16.457537 _ 0.085001 _ 8 5001 _ 0.01 _ 0.01 _ ' b. [33.00001] 2. (1 points) Use part a b to guess the instantaneous velocity of the athlete at t = 3 sec. 3. We want to evaluate the following limit: 1.x24 951533624. 2x8 a. (2 points) First find the limit by using a table and evaluating the function at values closer and closer to 2 from each side. (Hint: this process is MUCH EASIER ifyou use the TABLE function on your graphing calculator.) x f (x) x f (x) b. (1 points) What inference can you make about the limit? (Use limit notation] c. (1 2points) Use a graphing calculator to check your answer. Sketch the graph of x2 _ x2+2x4 8 (Make sure to label the asymptotes and holes. ) 4. (6 points) Sketch a function with the following features: a) f(-5) = 7 b) f(2) = 1 c) f (7 ) = 8 d) lim f(x) = 6 e) lim f (x) = -4 () lim f (x) = 4 x - 2 + x-2- x- 9 -10 1p g) (1 points) Given the information above, what can you say about lim f (x) ? x-2 Explain your answer.5. Consider the piece-wise function: h(x) =( x+2)2+1 if x 2 -2, ( |x + 2| + 1 if x