Problem Set Complete the following assignment and submit your work to the dropbox. Before you upload your file, ensure your name appears at the top of every page of your document. You may submit a scanned copy of handwritten pages or solutions typed on a word processor. Make sure you show your steps and submit full solutions to multi-step problems. 1. For the function f(x) = x* determine an approximation for the slope of the tangent to the curve at the point where x = 0.5. Use /(@+.) -(@), and h = 0.1. Show all your steps. 2. For the function f(x) = = find the slope of a tangent using lim f(Ith) -f(I) h+0 h Then find the actual slope of the function at the point where x=1. 3. A science project studying catapults sent a projectile into the air with an initial velocity of 30 m/s. The formula for distance (s) in meters with respect to time in seconds is 5 = -4.9t- + 30t. Find the instantaneous rate of change (and thus the velocity at any time) using lim {(a+!) -@) and then find the instantaneous rate of change at: a. t = 1 b. t = 3