Everything Maths Grade 12

7.2 CHAPTER 7. DIFFERENTIAL CALCULUS

x

y

7 − 5 − − 3 − (^11357)

1

3

− 1

− 3

Figure 7.2: Graph of y =^1 x.

As x→ 0 from the left, y =^1 xapproaches−∞. As x→ 0 from the right, y =^1 xapproaches +∞. This
is written in limits notation as:

lim x→ 0 −

1

x

=−∞

for x approaching 0 from the left and

lim x→ 0 +

1

x

=∞

for x approaching 0 from the right. You cancalculate the limit of many different functions using a set
method.

Method:

Limits: If you are required to calculate a limit like limx→athen:

Simplify the expression completely.

If it is possible, cancel all common terms.

Let x approach a.

Example 2: Limits

QUESTION

Determine lim x→ 1

10