ALGEBRA OF LIMITS

13.3.1 Algebra of limits

This section demonstrates the output of sum, difference, product and quotient of limits.

Let p and q be two functions such that their limits limx→a p(x) and limx→a q(x) exist.

Limit of the sum of two functions is the sum of the limits of the functions.

limx→a [p(x) + q(x)] = limx→a p(x) + limx→a q(x).

Limit of the difference of two functions is the difference of the limits of the functions.

limx→a [p(x) − q(x)] = limx→a p(x) − limx→a q(x).

Limit of product of two functions is the product of the limits of the functions.

limx→a [p(x) × q(x)] = [limx→a p(x)] × [limx→a q(x)].

Limit of quotient of two functions is the quotient of the limits of the functions.

limx→a [p(x) ÷ q(x)] = [limx→a p(x)] ÷ [limx→a q(x)].

Limit of product of a function p(x) with a constant, q(x) = α is α times the limit of p(x).

limx→a [α.p(x))] = α. limx→a p(x).

13.3.2 Limits of polynomials and rational functions

The limits of polynomials and rational functions are elaborated along with solved examples.