Everything Maths Grade 12

CHAPTER 7. DIFFERENTIAL CALCULUS 7.2

Activity: Limits

If f (x) = x + 1, determine:

f (− 0 .1)

f (− 0 .05)

f (− 0 .04)

f (− 0 .03)

f (− 0 .02)

f (− 0 .01)

f (0.00)

f (0.01)

f (0.02)

f (0.03)

f (0.04)

f (0.05)

f (0.1)

What do you notice about the value of f (x) as x gets close to 0?

Example 1: Limits Notation

QUESTION

Summarise the following situation by using limit notation: As x gets close to 1 , the value of

the function

y = x + 2

gets close to 3.

SOLUTION

This is written as:

lim

x→ 1

x + 2 = 3

in limit notation.

We can also have the situation where a function has a different valuedepending on whether x ap-
proaches from the left or the right. An exampleof this is shown in Figure 7.2.