# 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. [f(x)+g(x)] = f(x) + g(x) b) The limit of difference of two functions is nothing but the difference of the limits of the individual functions in the given order. [f(x)-g(x)] = f(x) – g(x) c) The limit of product of two functions is nothing but the product of the limits of the individual functions. [f(x)*g(x)] = f(x) * g(x) d) The limit of quotient of two functions is nothing but the quotient of the limits of the individual functions in the given order. [f(x)/g(x)] = f(x)/ g(x)**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.