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This has a right-hand limit and a left-hand limit,"},{"Start":"01:19.190 ","End":"01:22.189","Text":"the right-hand limit is b,"},{"Start":"01:22.189 ","End":"01:26.540","Text":"because the absolute value of h is equal to h on the right of 0,"},{"Start":"01:26.540 ","End":"01:29.210","Text":"but on the left absolute value of h is minus"},{"Start":"01:29.210 ","End":"01:34.494","Text":"h. We get the limit of minus b and the other side."},{"Start":"01:34.494 ","End":"01:36.735","Text":"Now, for the limit to exist,"},{"Start":"01:36.735 ","End":"01:42.460","Text":"both 1 sided limits have to be equal."},{"Start":"01:42.650 ","End":"01:45.830","Text":"It only exists if b is minus b,"},{"Start":"01:45.830 ","End":"01:48.335","Text":"which is the same as b equals 0."},{"Start":"01:48.335 ","End":"01:52.105","Text":"In this case the limit is 0."},{"Start":"01:52.105 ","End":"01:58.655","Text":"What we can say is that this is differentiable at 0, for b equals 0,"},{"Start":"01:58.655 ","End":"02:00.590","Text":"and for all values,"},{"Start":"02:00.590 ","End":"02:06.660","Text":"meaning arbitrary values of a and c. 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