This is True or False

1. If a function is itegrable then it must be differentiable. 2. The fact that f is an integrable function implies that there always exists a differentiable function, F(x), such that F'(x)= f(x). 3. lim- 20 2 = lim - 2x x -03x2 +x X-0 6x+1 3 4. If f'(a) =g'(a) then f(a)=g(a) + c where c is a constant. 5 . If functions f, and g are differentiable, and have a maximum distance between the two functions at x=a, then f'(a)= g'(a). 6. 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. 7. There are only 2 types of asymptotes: horizontal, and vertical asymptotes. 8. If a function is differentiable, then it must be continuous. 9 . Since f(x)=1/x is continuous on (0, 1), it it integrable on [0, 1]. 10. lim x* =0. 11. Every bounded continuous function is integrable. 12 f(x)=|x| is not integrable in [-1, 1] because the function f is not differentiable at X=0. 13 If f(x)