Question

How do you find the limit of `[e^(3x2-12x+12)] / (x^4-16)` as x approaches 2?

Answer 1

The limit does not exist.

Explanation:

As `xrarr2`, the exponent `3x^2-12x+12 rarr 0`.

So the numerator goes to `1`.

meanwhile the denominator goes to `0`.

The limit does not exist.

An investigation of the sign will reveal that

as `xrarr2` from the left the quotient decreases without bound:

`lim_(xrarr2^-)e^(3x^2-12x+12)/(x^4-16) = -oo` and

as `xrarr2` from the right the quotient increases without bound:

`lim_(xrarr2^+)e^(3x^2-12x+12)/(x^4-16) = oo`