Calculus Examples

$\frac{lim_{x \to 4} 9}{x^{2} - 8 x + 16}$

Step 1

Evaluate the limit of $9$ which is constant as $x$ approaches $4$ .

$\frac{9}{x^{2} - 8 x + 16}$

Step 2

Factor using the perfect square rule.

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Step 2.1

Rewrite $16$ as $4^{2}$ .

$\frac{9}{x^{2} - 8 x + 4^{2}}$

Step 2.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$8 x = 2 \cdot x \cdot 4$

Step 2.3

Rewrite the polynomial.

$\frac{9}{x^{2} - 2 \cdot x \cdot 4 + 4^{2}}$

Step 2.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 4$ .

$\frac{9}{{(x - 4)}^{2}}$