Question

How do you evaluate the limit `(x^2+4x+2)/(x^2-3)` as x approaches `-3`?

Answer 1

By substitution.

Explanation:

Since `lim_(xrarr-3)(x^2-3) != 0` we can simply find the quotient of the limits,

`lim_(xrarr-3)(x^2+4x+2)/(x^2-3) = (lim_(xrarr-3)(x^2+4x+2))/(lim_(xrarr-3)(x^2-3))`

`= ((-3)^2+4(-3)+2)/((-3)^2-3) = -1/6`