Question

Evaluate the following limits :
lim x 2 x² - 4/-x-2​

Answer 1

Explanation:

If we look at the graph of

y

=

x

2

−

4

x

−

2

we can see that it is clear that the limit exists, and is approximately

4

graph{(x^2-4)/(x-2) [-10, 10, -5, 5]}

The numerator is the difference of two squares, and as such we can factorise using it as

A

2

−

B

2

≡

(

A

+

B

)

(

A

−

B

)

Se we can factorise as follows:

lim

x

→

2

x

2

−

4

x

−

2

=

lim

x

→

2

x

2

−

2

2

x

−

2