# Basic Theroems on Limits

In this tutorial we give the statements of theorems on limits which will be useful in evaluating limits.

**(1)** The limit of a function, if it exists, is unique.

**(2)** If and are any constants, then .

**(3)** If is a constant, then for any number , .

**(4)** For any constant and , we have

**(5)** The limit of the sum of two functions is equal to the sum of their limits, i.e. and , then

**(6)** The limit of the difference of two functions is equal to the difference of their limits, i.e. and , then

**(7)** The limit of the product of two functions is equal to the product of their limits, i.e. and , then

**(8)** The limit of the quotient of two functions is equal to the quotient of their limits, provided the limit of the denominator is not zero, i.e. and , then

**(9)** If is any integer and , then

__Sandwich Theorem__

If for all numbers in an open interval containing a except possibly at a itself, such that

then