Question

27.) If a ≠ 0, then lim (x^2 - a^2)/(x^4 - a^4) is: x->-a

Answer 1

Answer:

$\frac{1}{2a^2}$

Step-by-step explanation:

Step 1: Write limit

$\lim_{x \to -a} \frac{x^2-a^2}{x^4-a^4}$

Step 2: Factor

$\lim_{x \to -a} \frac{(x+a)(x-a)}{(x+a)(x-a)(x^2+a^2)}$

Step 3: Simplify

$\lim_{x \to -a} \frac{1}{x^2+a^2}$

Step 4: Substitute

$\frac{1}{(-a)^2+a^2}$

Step 5: Evaluate

$\frac{1}{a^2+a^2}$

Step 6: Simplify

$\frac{1}{2a^2}$