Ifg{x) :1 x) 5 Mac) for all x at c in some interval about c. and 11111905] = lint Mac) = L, x-c XH' then lim flfx) = L. XH' 1. In this problem you will use the squeeze theorem to determine lim xzemsej xm a) Use technology to determine the range of cos G). Justify your answer with a table of values or a sketch. b) Write a compound inequality with the range of cos C?) in the middle. Exponentiate all three components. For example, 1 S sin(x) S 1 would become 9'1 5 95mm 5 91. Does this compound inequality satisfy the conditions of the squeeze theorem? Justify your answer with a table of values or a sketch. 0) Multiply each component of the compound inequality by x2. Does this compound inequality satisfy the conditions of the squeeze theorem? Justify your answer with a table of values or a sketch. d) If the initial conditions are met, determine the limit using the squeeze theorem. Be sure to use the correct limit notation. 1.A function y = JHair) that is continuous on a closed interval [a,b] takes on every value between Ha) and {(b). In other words, if yo is between {(a) and b), then yo = c) for some r: in [a,b]. 2. Construct a function where the initial conditions for the intermediate value theorem fail. Justify your answer with a table or sketch of the function, and an explanation of whythe theorem cannot be applied. 3 3. Use the intermediate value theorem to show that :71 = 4 x is solvable. Be sure to conrm that the initial conditions have been met. 4. Is the converse of the intermediate value theorem true? (Converse: If there exists a value c on the closed interval [(1,1)] such thatc) = ya for every yo between n.) and Kb), then y = f(x) is continuous.) Give a counterexample if the converse is false, and justify your