Q Questions 1. Using Desmos/Excel or other graphing software sketch the graph of f(x) = sin(2x). a. Using tangents set up a table of values for X f' (x) -n -3n1/4 -n/2 -n/4 2n 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) ?3. Find the derivative of the following functions using the "definition of the derivative" proof with the expression lim f(xth) - f(x) h-> 0 h Show all your steps. a. f ( x ) = x2 + 3x b. f (x ) = 2 x5. A radioactive isotope has a half life of 30 years. The initial amount is 10 mg. 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.2. Using Desmos/Exoel or other graphing software sketch the graph of f(x) = 4" a. Using tangents set up a table of values for b. Plot the points and nd a function that will join the points to form a continuous curve. C. What is the equation for the derivative of m) = 4* 4. State the derivative of the following functions. a) f(x) = 10x b) f(x) = 2x c) f(x) = Cos x d) f(x) = -sin(3x)