Q. 8 - Calculus

Question

what it means for a function f to be continuous on a closed interval [a, b], or continuous on an open interval (a, b), or continuous on a half-closed interval [a, b) 

Step-by-Step Solution

Answer

If the function is continuous at every interior point and endpoint of the interval then the function f is continuous on a closed interval $[a,b].$

If Function is continuous only at interior points of an interval then the Function f is continuous on an open interval $(a,b).$ 

if the function is continuous only at interior points and the left endpoint $x=a$then the Function f is continuous on a half-closed interval $[a,b).$

Step 1. Given information.

Function f is continuous on a closed interval $[a,b].$

Function f is continuous on an open interval $(a,b).$

Function f is continuous on a half-closed interval $[a,b).$

Step 2. Explanation

If the function is continuous at every interior point and endpoint of the interval then the function f is continuous on a closed interval $[a,b].$

If Function is continuous only at interior points of an interval then the Function f is continuous on an open interval $(a,b).$

if the function is continuous only at interior points and the left endpoint $x=a$then the Function f is continuous on a half-closed interval $[a,b).$