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basic definition of a limit
 lim x > c f(x) = L
 as x gets closer and closer to c, but not equal to c, the values of f(x) get closer and closer to the value L

continuity
 a function f is continuous at a point x = c if
 lim x>c f (x) = f (c)
 (it has no holes, jumps or gaps)

differentiability
 a function f is said to be differentiable at x = c if the limit
 lim x>c (f(x)  f(c)) / x  c exists
 (at any point there is a well defined tangent line, smooth, no sharp points)
 *if differential it must be continuous (but reverse isn't true)

Factor (A + B)^{3}
A^{3} + 3A^{2}B + 3AB^{2} + B^{3}

