course Mth 271
Will you please help me understand weither or not a function is contiuous?..I am having a lot of problems with this?When I am finding a limit I just plug in the whatever is under the lim and solve the equation?.right?
If the function is continuous you can just plug in and solve the equation. However if there's a question of continuity, you have to compare what you get when you plug in the number with what you get when you evaluate the function at nearby numbers. For example the limit of a function as x -> 3 is determined not by the value at x = 3, but by values close to x = 3 (e.g., 2.9, 2.99, 2.999, ... and also 3.1, 3.01, 3.001, ...). In general you would ask what the value is at x = 3 + `dx, and consider what happens as `dx shrinks toward 0.
If you have questions on specific problems I'll be glad to answer them.