Derivative
Geometrically, the derivative of a function can be interpreted as the
slope of the graph of the function or, more precisely, as the slope of
the tangent line at a point. It is calculated from the slope formula
Limit
The limit is the value that a function "approaches" as the input
"approaches" some value. For example, the limit of f at x = 3 is the
value f approaches as we get closer and closer to x = 3- Graphically,
this is the y-value we approach.
What this means, is that even when x
gets closer and closer to 3 then value
of f will get closer and closer to 5, we
can’t say that y = 5 when x= 3. So yet
the limit of f at x = 3 is 5, the value of
f at x = 3 is undefined
Diagram shows that y changes from
to , applying this to formula: