What is a limit ? When does a limit exist? Continuity Continuity of basic algebraic functions Algebra of limits The case 0/0

What is a limit? A limit of a function is an intended “height” of a function at a point Lim f (x) = 4 X  2

When does a limit exist?

f (x) = x²

When does a limit exist?

With a plus sign

When does a limit exist? With a minus sign

In order to have a limit at a point At that point: Left limit MUST EQUAL Right limit Lim f (x)= 1 X  4ˉ X  4 Lim f (x)= 1 X  4 With no sign +

Limit exist Lim f (x)= 1 X  4

Infinite Limits ( are not limits)

How to evaluate a limit, in case of algebraic functions? 1.Finding the value of the function at the point (Substitution in the formula of the function) If the function is continuous at the point 2.Factoring 3.The Conjugate Method

Substitution

Factoring

The Conjugate Method What is a conjugate? X-16 = (√x - 4) (√x + 4) AND (√x + 4) is the conjugate of (√x - 4) respect to X-16 (√x - 4) is the conjugate of (√x + 4) respect to X-16

The Conjugate Method

Continuity A function f is continues at a if lim f (x) = f (a)

Continuity lim f (x) = 4 = f (2) X  2 4, x≤2 f (x) 2x, x > 2 {

Continuity from the right lim f (x) = 4 = f (2) X  2+

Continuity from the left lim f (x) = 4 = f (2) X  2ˉ

Discontinuity A function is discontinues at a if the limit is not equal to the value f (a) A continuous function should have: 1.no breaks in the graph 2.no holes 3.no jumps