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Hello, please help answer number 2,3 and 6. Thank you very much! Please also provide explanations and working.

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Screen Shot 2020-02-11 at 11.23.41 PM (2).png

6. (1pt) Suppose that f is a continuous function on [0, 2] such that f(0) = f(2). Show that there
must be a number c E [1, 2] such that f(c) = f(c - 1).
[Hint: Let g(x) = f(x) - f(x - 1) and apply the Intermediate Value Theorem.

Screen Shot 2020-02-12 at 2.30.43 AM (2).png

2. (1pt) Evaluate the limit
|20 - 2
x--2Vx2 -3-1
3. (1pt) Given that the function g(x) is defined on R by
g (20) =
x . sin x . cos -2
72 , if x70
, if x = 0
What should be the value of A if g(x) is continuous at x = 0? Explain your work and justify
your answer.

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