Finding limits algebraically  direct substitution
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.
Lessons
Notes:
if: a function $f$ is continuous at a number $a$
then: direct substitution can be applied: $\lim_{x \to a^} f(x) = \lim_{x \to a^+} f(x) = f(a)$
note: polynomial functions are continuous everywhere, therefore “direct substitution” can always be applied to evaluate limits at any number.

a)
State the value of the limit from the graph of the function $f\left( x \right) = \frac{1}{{x  2}}$
 $\lim_{x \to 3} f(x)$
 $\lim_{x \to 2.5} f(x)$
 $\lim_{x \to 0} f(x)$ 
b)
Evaluate:
 $f(3)$
 $f(2.5)$
 $f(0)$


2.
Evaluate the limit:

3.
Evaluate the onesided limit:

a)
$\lim_{x \to {1^  }} g(x)$
$\lim_{x \to {1^ + }} g(x)$
$\lim_{x \to {1}} g(x)$ 
b)
$\lim_{x \to {4^  }} g(x)$
$\lim_{x \to {4^ + }} g(x)$
$\lim_{x \to {4}} g(x)$
