Continuity is fairly easy to understand. A function whose graph does not have any breaks in it will be continuous. Discontinuities are a little more complicated, but not by much. The only thing that makes discontinuities slightly more confusing is the different types: jump, removable and infinite.
Problems:
1. Using the substitution method, evaluate the limit of cos^(-1) (x/9) as x approaches 9.
To solve I plugged 9 in for x giving me the limit of cos^(-1) (9/9) as x approaches 9, which is also equal to lim cos^(-1) (1) as x approaches 9 = 0.
2. What is the domain of the function and is it continuous on its domain? f(x) = square root of (x^2+64)
For this problem x can be any number greater than or equal to 8. For any number less than 8, the function will be discontinuous.
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