1. Slopes of tangent lines For the following functions, make a table of slopes of secant lines and make a conjecture about the slope of the tangent line at the indicated point. f(x)=3x-x at x=1 2. Impact speed A rock is dropped off the edge of a cliff, and its distance s (in feet) from the top of the cliff after t seconds is s(t)=16t^2. Assume the distance from the top of the cliff to the ground is 96ft a. When will the rock strike the ground? b. Make a table of average velocities and approximate the velocity at which the rock strikes the ground. 16. What are the potential problems of using a graphing utility to estimate lim f(x)? 18. One-sided and two-sided limits Use the graph of g in the figure to find the following values or state that they do not exist. If a limit does not exist, explain why. a. g(2) . lim_ g(x) lim. 9(x) d. lim g(x) 9(3 f. lim_ g(x) g. lim, g(x) h. g(4) i. lim g(x) y = 8(x) 33. Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. x2 -9 a. The value of lim - does not exist. b. The value of lim f(x) is always found by computing f(a). . The value of lim f(x) does not exist if f(a) is undefined. d. lim vx = 0. (Hint: Graphy= Vx .) e. lim cotx =0. (Hint: Graphy = cotx.) 34. The Heaviside function The Heaviside function is used in engineering applications to model flipping a switch. It is defined as H ( x )=10 ifx