Limits

**CalculusKing** · May 20th 2009, 03:55 PM

Find the limit, if it exists.

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

**Plato** · May 20th 2009, 03:59 PM

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.

**matheagle** · May 20th 2009, 10:40 PM

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

**HallsofIvy** · May 21st 2009, 04:06 AM

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

**matheagle** · May 21st 2009, 01:47 PM

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.

**Plato** · May 21st 2009, 02:51 PM

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.

Thread: Limits