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)x. 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)*? (Note: The equation of the derivative will be of the form y = k(0.75)*.)3. Find the derivative of the following functions using the lim fxth) - f(x) a. f (x) = x2 + 5x 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