Hello I need some help with these 5 questions. If you could please show me all your work on a separate sheet of paper with the solutions/answers that would be great!

1. Using Desmos/Excel or other graphing software sketch the graph of 2. Using Desmos/Excel or other graphing software sketch the graph of f(x) = sin(2x). (x) = 4x a. Using tangents set up a table of values for a. Using tangents set up a table of values for f(x) '(x) -3 n/ -2 -1/2 -11/4 0 2n w 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) ? 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) = 4x 3. Find the derivative of the following functions using the "definition of the derivative" proof with the expression 4. State the derivative of the following functions. lim f( x + h) - f(x) a) f(x) = 10* Show all your steps. b) f(x) = e2x a) f(x) = x2+ 3x c) f(x) = cos x d) f(x) = -sin(3x) 5. A radioactive isotope has a half life of 30 years. The initial amount is 10 mg. b ) f ( x ) = 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 in 65 years from now? c. Show a graph of the quantity of isotope over 100 years