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Continuous

is a quantitative variable that has a continuum of infinitely many possible values

Differentiable

The function is differentiable at 'a' if f '(a) exists. A function is not differentiable at pivot points. (If f(x) is differentiable at 'a' it is continuous at 'a')

limit

The unique value that a function approaches as x-values of the function approach c from the left and right sides

inverse function

Let f be a one-to-one function with domain A and range B. Then its ________________ f^-1 has domain B and range A and is defined by f^-1 (y) = x, f(x)=y for any y in B

Properties of Inverse Functions

f(f^-1(x)) = x f^-1(f(x)) = x If f(a) = b and f '(a) = c then (f^-1(b))' = 1/c OR (f^-1) '(a) = 1 / (f '(f^-1(a))

Restricted Domain of Inverse Trig Functions

arcsin(x) -> -pi/2 <= x <= pi/2

Derivatives of Inverse Functions

arcsin(x) = 1/sqrt(1-x^2) arccsc(x) = -1/x*sqrt(x^2-1)