Question

(5x 2 −8x−13)
lim x→3 ​ ( x 2 −5 )​

Answer 1

Resposta:

que(????? ???????????

Answer 2

Resposta:

How do you find the limit of

5

x

2

−

8

x

−

13

x

2

−

5

as x approaches 3?

Calculus Determining Limits Algebraically

1 Answer

Jim H

Mar 6, 2015

Use the properties of limits.

lim

x

→

3

(

x

2

−

5

)

=

lim

x

→

3

x

2

−

lim

x

→

3

5

(Subtraction property)

=

(

lim

x

→

3

x

)

2

−

lim

x

→

3

5

(Power property)

=

3

2

−

5

(Limits of Identity and constant functions)

=

9

−

5

=

4

(Arithmetic)

Because the limit of the denominator is not

0

, we can use the quotient property for limits.

By steps similar to those above, we can show that

lim

x

→

3

(

5

x

2

−

8

x

−

13

)

=

5

(

3

)

2

−

8

(

3

)

−

13

=

45

−

37

=

8

.

And, therefore

lim

x

→

3

5

x

2

−

8

x

−

13

x

2

−

5

=

8

4

=

2

.