Calculus for Cognitive Scientists by James K. Peterson

Author:James K. Peterson
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

The value B is usually denoted by the symbol and the right and left hand limits are then denoted by and , respectively. It is possible for the derivative to exist on an interval, but fail to be continuous at some point in the interval. Consider this function f

The function and so we have removed the discontinuity f would normally have at by defining it to have that value at 0. Then f is continuous at 0 and we have for that

Then, we find

Now make a change of variable and let . Then the above limit changes to

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