# Limits: Reaching for a Goal

A limit can be a difficult concept to grasp in mathematics, as it is a value that is never reached, but is ‘approached’ by an input, or index of some nature. Limits are essential for integrals, continuity and derivatives in calculus.

Let f(x) be a given function. Values of f(x) can be made arbitrarily close to L. We can do this by taking x sufficiently close to a, with x≠a, on either side of a, then we say that L is the limit of f(x) as x approaches a and we write it as f(x) = L.

If xà∞ then it means that x values will go far on the right side of the horizontal axis, x-axis. The corresponding f(x) values will be read on the vertical axis, Y-axis. To understand this we can examine the following examples.

**Calculation of limits:**

a) The limit of sum of two functions is nothing but the sums of the limits of the individual functions.

b) The limit of difference of two functions is nothing but the difference of the limits of the individual functions in the given order.

c) The limit of product of two functions is nothing but the product of the limits of the individual functions.

d) The limit of quotient of two functions is nothing but the quotient of the limits of the individual functions in the given order.

**Situations where a limit cannot be found:**

a) The limit of a difference of functions cannot exist if both tend to ∞.

b) The limit of product of two functions cannot exist of one tend to ∞ and the other tend to 0.

c) The limit of quotient of two functions cannot exist if both tend to either ∞ or zero.

Need further help with Math?

SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Delaware visit: Tutoring in Delaware.