Functions, Limits, Continuity and Differentiability
Single variable calculus deals with functions of one variable, multivariable calculus deals with functions of multiple variables.
Limits
A limit is the value f(a) that a function f(x) approaches as that function’s inputs 'x' get closer and closer to some number 'a'. The idea of a limit is the basis of all calculus.
Continuity
A function f(x) is continuous on a set if the graph of f is a connected curve without any jumps, gaps, or holes.
Continuity can be defined using the concept of limits where a continuous function will satisfy the following equation:
Differentiability
A function is differentiable at a point if it has a derivative there. Note: A differentiable function must be continuous
The function f is differentiable at x if the derivative exists:
Test for differentiablity:
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