# Finding limits algebraically - direct substitution

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###### Topic Notes

Graphically finding the limit of a function is not always easy, as an alternative, we now shift our focus to finding the limit of a function algebraically. In this section, we will learn how to apply direct substitution to evaluate the limit of a function.

• if: a function $f$ is continuous at a number $a$

then: direct substitution can be applied: $\lim_{x \to a^-} f(x) = \lim_{x \to a^+} f(x) =\lim_{x \to a} f(x)= f(a)$

• Polynomial functions are continuous everywhere, therefore "direct substitution" can

then: direct substitution can be applied: $\lim_{x \to a^-} f(x) = \lim_{x \to a^+} f(x) =\lim_{x \to a} f(x)= f(a)$

• Polynomial functions are continuous everywhere, therefore "direct substitution" can

**ALWAYS**be applied to evaluate*limits*at any number.2

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