L'Hopital's rule problem

[medicalphysicsguy]

Evaluate lim x->1

for (x^3-3x+2)/(x^2-2x-1)

I use L'Hopitals once and get:

(3x^2-3)/(2x-2)

Still indeterminate so I use it again and get:

6x/2

I get answer is 3

Book says answer is zero.

Can anyone explain? I am doing the other problems in the section okay.

Thanks!

 

[srmichael]

Evaluate lim x->1

for (x^3-3x+2)/(x^2-2x-1)

I use L'Hopitals once and get:

(3x^2-3)/(2x-2)

Still indeterminate so I use it again and get:

6x/2

I get answer is 3

Book says answer is zero.

Can anyone explain? I am doing the other problems in the section okay.

Thanks!

You don't have to use L'Hopital's rule since the limit as x goes to 1 of x^2-2x-1 is not 0...it is -2

 

[SAMUELK]

You don't have to use L'Hopital's rule since the limit as x goes to 1 of x^2-2x-1 is not 0...it is -2

You are being too nice. The proper answer is

You MAY NOT use L'Hopital's rule since the limit as x goes to 1 of x^2-2x-1 is not 0...it is -2.

L'H's rule applies to 0/0 or inf/inf limits, which the original is not.