1. ## Limits

Find the limit, if it exists.

limit as x approaches 2 (x^3+x^2-14x+16)/(x-2)

2. Originally Posted by CalculusKing
Find the limit, if it exists.
limit as x approaches 2 (x^3+x^2-14x+16)/(x-2)
If $x=2$ is a zero of $x^3 +x^2 -14x +16$ then $(x-2)$ is a factor.

3. I wouldn't divide. This is of the form 0/0, so I would use l'Hopital's Rule to quickly solve this.

4. I, on the other hand, would prefer Plato's method. It requires less "sophisticated" machinery.

5. Originally Posted by HallsofIvy
I, on the other hand, would prefer Plato's method. It requires less "sophisticated" machinery.

I agree, but I hate division.
It's good to see both ways though.
I do half of the l'hopital problems in calc 2 via calc 1 techniques.

6. Originally Posted by matheagle
I agree, but I hate division.
It's good to see both ways though.
I do half of the l'hopital problems in calc 2 via calc 1 techniques.
Please don’t forget that many problems on limits appear in calculus textbooks before differentiation is ever introduced.