Let f(x) be defined on an interval (a,b) and suppose that f(c) #0 at some c where f(x) is continuous. Show that there is an interval (c-6,c +6) about c where f has the same sign as f(c). From the definition of continuity, what is known about the function? f(c) exists O lim f(x) exists x-c O lim f(x)=f(c) x O All of the above. Which of the following statements is the condition of a limit? OA. A limit f(c) exists if, for every number e > 0, there exists a corresponding number 8>0 such that for all x, 0< x − c | < 8 → [f(x) − f(c)| < e. OB. A limit f(c) exists if, for every number 8>0, there exists a corresponding number e > 0 such that for all x, 0< |x − c | < 8 → [f(x) – f(c)| 0, there exists a corresponding number 8>0 such that for all x, 0< |x-c| < 8 → |f(x)-f(c) >c OD. A limit f(c) exists if, for every number 8>0, there exists a corresponding number >0 such that for all x, 0< |x-c|< 6→ [fix)-f(c)| > E Which of the following equalities could be used in the definition of the limit to show that there is an interval (c-8,c +8) about c where f has the same sign as f(c). O 8= |f(c)| e= |c| e= |f(c)| O 8 c Which of the following statements is the correct interpretation of these equations? O A. In the inequality 0