Solving L'Hospital's Rule: lim(x→2)(x^2+x-6)/(x-2)

[phillyolly]

Homework Statement

lim(x→2)(x^2+x-6)/(x-2)

Homework Equations

The Attempt at a Solution

lim(x→2)(x^2+x-6)/(x-2)=lim(x→2)(d/dx(x^2+x-6))/(d/dx(x-2))=lim(x→2)(2x+1)/1=lim(x→2)(2x+1)=5

Is this a right solution? I have never done such before, so I am not sure in my answer.

 

[Dick]

It's fine if you've checked you have a 0/0 form to begin with. You could also factor x^2+x-6 and cancel the denominator to check.

 

[renrenbin]

yeaa, it is a right way,absolutely.L'Hopital's Rule is for 0/0 and inf/inf.

 

[phillyolly]

Thank you a lot, guys.