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Explain clearly why you would suspect from these values that the derivative of sin x is cos x. Find the derivative of y = sin x (x in radians) algebraically. EMBED Equation.2 Use the limits in part # 1 to get the result. Explain your work. (Note: sin(x + h) = sin x cos h + sin h cos x) (c) repeat part (b) for the function y = cos x (x in radians) (Note: cos(x + h) = cos x cos h - sin x sin h) Part #3. Differentiability and Continuity. Consider the graph of each function. Use a table to estimate EMBED Equation.DSMT4 or determine that it doesnt exist, for each c. (See sample table below.) Confirm that your answer is reasonable by looking at the graph. (a)  EMBED Equation.DSMT4  c = 1 c = -3 (b)  EMBED Equation.DSMT4  c = 1 c = 0 Based on your experimentation, can you establish some criteria so that you can look at a graph and determine where the derivative does and does not exist? Perhaps further experimentation would help. Optional: Consider EMBED Equation.DSMT4  c = -1 What does your experimentation tell you about the relationship between differentiability and continuity? ---------------------------------------------------------------------------------------------------------------------------------------------   EMBED Equation.DSMT4  c = 1  EMBED Equation.DSMT4  Explain. (Note: One way of filling in the table is by placing f(x) in y1 in your TI-89 calculator. Then from the home screen enter: (y1(1+h) y1(1))/h | h =1. After you get one value, just edit a previous command for others.) Lab report: 1 per group.    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