1. Using graphing software sketch the graph of f(x) = sin(2x). (https://www.desmos.com/calculator/uzbyymkirs) a. Using tangents set up a table of values for X slope of tangent of f(x) -P -3p/4 -p/2 -p/4 . . . 2p b. Plot the points for the slope of the tangent and find a function using technology that will join the points to form a continuous curve. Include a picture showing the original graph and a tangent to the graph with your solution. c. What is the equation for the derivative of f(x) = sin(2x)? 2. Complete a similar process for the equation f(x) = (0.75)*. a. Using tangents set up a table of values for X slope of tangent of f(x) -8 -6 -4 -2 . . . 6 b. Plot the points for the slope of the tangent and find a function using technology that will join the points to form a continuous curve. Include a picture showing the original graph and a tangent to the graph with your solution. c. What is the equation for the derivative of f(x) = (0.75)*?3. Find the derivative of the following functions using the lim f(x th) - f (x) a. f( x) = x2+ 5* b. f (x)= 1 Show all your steps. 4. Show that lim (ex - 1) = Ine = 1 using at least two numerical examples. 5. List two real life applications than can be modeled by the exponential function f(x) = ex