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if the limit of f(x) as x approaches 2 is equal to 4, what is the limit of (f(x) -4)/(x-2) as x approaches 2?​

User Mike Bretz
by
8.6k points

1 Answer

3 votes

Answer: lim

x

2

x

2

4

x

2

=

4

Step-by-step 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

=

lim

x

2

(

x

+

2

)

(

x

2

)

x

2

=

lim

x

2

(

x

+

2

)

x

2

x

2

=

lim

x

2

(

x

+

2

)

=

(

2

+

2

)

=

4

User Alex Robertson
by
7.8k points

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