10. 11. Describe circumstances when the limit of a sequence exists, and when it does not exist. What information do the left-hand limit and right-hand limit provide about the graph of a function? How can you tell if a function is continuous or discontinuous from its graph? How do limit help determine if a function is continuous? a) Discuss the differences and similarities between the formula mmn = lim f (a+h)-f (h) hm h b) What does the derivative represent? What does it mean when we say that the derivative describes a new function? Support your answer with an example c) What is the relationship between the domain of the original function and the domain of the corresponding derivative function? Provide an example to support your answer. a) How can a function have a limit, L, as x approaches a, while f (a) at L? b) Given an example of a mction whose limit exists at x = a, but which is not dened at x = a. c) How are the limit properties useil when evaluating limits algebraically? d) Describe the types of discontinuities that a graph might have. Why do the names of these discontinuities make sense? and the rst principles denition for the derivative