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limit

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

Basic Limits

lim k = k

Scalar Multiple

lim [b f(x)] = bL

Sum or Difference

lim [f(x) +/- g(x)] = L+/- K

product

the answer to a multiplication problem

quotient

the answer to a division problem

power

a number produced by raising a base to an exponent

Limits of Polynomial and Rational Functions

If p is a polynomial function and c is a real number then

Limit of a Function Involving a Radical

Let n be a positive integer. The following limit is valid for all c if n is odd, and is valid for c > 0 if n is even

Limit of a Composite Function

If f and g are functions such that lim g(x) = L and lim f(x) = f(L),

Squeeze Theorem

If h(x)<_ f(x)<_ g(x) for all ox in an open interval containing c, except possibly at c itself and if lim h(x) = L = lim g(x)