Please answer the following neatly and clearly.

NOTE- for question 1) follow the instructions CLOSELY and screenshot your work.

1. Using Winplot or other graphing software sketch the graph of y = sin(2x). (Unit 3 Activity 1 has instructions on the use of Winplot.) a. Using tangents set up a table of values for X f' (x) -p -3p/4 -p/2 -p/4 . .. 2p b. Plot the points and find a function that will join the points to form a continuous curve. c. What is the equation for the derivative of f(x) = sin(2x)? 2. Complete a similar process for the equation y = (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 / (x +4) - /(x) a. f(x) = x2+5* b. f ( x ) = Show all your steps. 4. A radioactive isotope has a half life of 30 years. If we started off with 10 mg of this isotope 12 years ago: a. Find an expression for the amount of the isotope that is still active using time t measured in years. b. How much of the isotope do we have at the present time? c. What is the present instantaneous rate of decay? Show a solution using the lim: f(xth)- j(xx) ? d. Show a graph of the quantity of isotope over 100 years. 5. Show that lim (e" -1) _ me= 1 using at least two numerical examples. h 6. Given f(x) = e", verify that jim-e) =* and explain how this illustrates that f'(x) = In e . f(x) = f(x). h 7. List two real life applications than can be modeled by the exponential function f(x) = ex