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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,

[tex]\lim_{x \to c}f(x) = m[/tex]

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:

[tex]\lim_{x \to c}f(x) = f(c)[/tex]

(See explanation)

Equations

Identities of limits:

[tex]\lim_{x \to c}f(x) + g(x) = \lim_{x \to c}f(x) + \lim_{x \to c}g(x)[/tex]...

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