Question

Why _{x\to -3}\left(x^2-2x+4\right)" alt="\lim _{x\to -3}\left(x^2-2x+4\right)" align="absmiddle" class="latex-formula"> is 19 and not 1??? I don't understand how lim x to -3 (x^2) become 9 and not -9???
PLEASEEEEEEEEEEEEE

Answer 1

The quadratic is continuous over its entire domain, which is to say we can evaluate the limit by direct substitution:

$\displaystyle \lim_{x\to-3} (x^2 - 2x + 4) = (-3)^2 - 2(-3) + 4 = 9 + 6 + 4 = \boxed{19}$

You are mistaking (-3)² for -3². They are not the same number.

(-3)² = (-1 × 3)² = (-1)² × 3² = 1 × 9 = 9

-3² = -1 × 3² = -1 × 9 = -9