Question

How do you evaluate the limit `(x+3)/(2x^2+2x+1)` as x approaches `3`?

Answer 1

By substitution.

Explanation:

If `x` is close to `3`, the `x+3` is close to `6` and

`2x^2+2x+1` is close to `2(3)^3+2(3)+1 = 25`.

So the quotient is close to `6/25`.

`lim_(xrarr3) (x+3)/(2x^2+2x+1) = 6/25`