Finding limits algebraically - direct substitution
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: limx→a−f(x)=limx→a+f(x)=limx→af(x)=f(a)
• Polynomial functions are continuous everywhere, therefore “direct substitution” can ALWAYS be applied to evaluate limits at any number.
No more finding limits “graphically”; Now, finding limits “algebraically”!
When to apply Direct Substitution, and why Direct Substitution makes sense. Exercise:f(x)=x−21
i) Find the following limits from the graph of the function. limx→3f(x) limx→2.5f(x) limx→0f(x)
ii) Evaluate: f(3) f(2.5) f(0)