Definition/Summary
Limits are a mathematical tool that is used to define the ‘limiting value’ of a function i.e. the value a function seems to approach when its argument(s) approach a particular value. Although the argument of the function can be taken to approach any value, limits are helpful in cases where the argument approaches a value where the function is not defined or becomes exceedingly large.
While defining a limit, we say that the argument ‘tends to’ a value. For example,
$$\lim_{x \to c}f(x) = m$$
is said: “As x tends to c, the function f(x) tends to m”. This statement however makes no assertion of what the value of f(c) would be. Rather, it means that as x becomes exceedingly close to ‘c’, f(x) becomes exceedingly close to m.
If, however, the function is defined and continuous at ‘c’, then:
$$\lim_{x \to c}f(x) = f(c)$$
(See explanation)
Equations
Identities of limits:
$$\lim_{x \to c}f(x) + g(x) = \lim_{x \to c}f(x) + \lim_{x \to c}g(x)$$...