1. (30%) True and False 1. Adr = [-1' , =-2 . 2. If f is continuous then _ _ f(t)dt = f(x). 2x -5 6x2 lim- lim - 1 49 x-27 x-9 3x- = 2 3. 4. The fact that f is an integrable function implies that there always exists a differentiable function, F(x), such that F'(x)= f(x). 5. " [ (31 + 2)dt = (3x7+2) 6. If f'(a) =g'(a) then f(a)=g(a) + c where c is a constant. 7. If functions f, and g are differentiable, and have a maximum distance between the two functions at x=a, then f'(a)= g'(a). 8. If f(x) is continuous on a closed interval I , and f(a) and f(b) have opposite signs where a and b are in I, then there exists a value c in [a, b] such that f (c) =0. 9. There are only 2 types of asymptotes: horizontal, and vertical asymptotes. 10. If a function is differentiable, then it must be continuous. 11. Since f(x)=1/x is continuous on (0, 1), it it integrable on [0, 1] 12 lim x* =1. X+0 13. Every bounded continuous function is integrable. 14. f(x)= |x| is not integrable in [-1, 1] because the function f is not differentiable at x=0. 15. If f(x)