Please write neatly; thank you.

6. A continuous function g has the values: I 1 2 3 4 5 6 'F 3(1'} 3 1 4 1 3 2 1 (a) g has at least roots between 1 and 5. {b} 3*{1'} = 3.2 in at least places between I = 1 and .r = 1?. {c} 3*{1'} = .'.? in at least places between x=33x= (d) 3*{1'} = 1.3 in at least places betwea'i x=mx= {e} Is it possible for 30:} to equal FT for some a:- yaluelfs} between 5 and 6? 1'. Section [1.4, problem 2? 3'? Starting with x = 1, do the iterates of x} = % approach a number? What happens if you start withx=l1.50r:r=4? 3. Section [1.4, problem 25 26. Let x} = 1 +sinfx}. {a} What happens if you start with x = 1 and repeatedly feed the output from f back into f? {b} What happens if you start with x = 2 and examine the iterates of f? 9. Section (1.4, problem 1? 17. Find A and B so that f (g(x)) = g (f(x) ) when: (a) f(x) = 3x + 2 and g(x) = 2x + A (b) f(x) = 3x + 2 and g(x) = Bx - 1 10. Section 1.3, problem In 12-17, use the IVT to verify each function has a root in the given interval(s). Then use the Bisec- tion Algorithm to narrow the location of that root to an interval of length less than or equal to 0.1. 12. f(x) = x2 -2 on [0,3]