Answer:
[tex]\frac{1}{2a^2}[/tex]
Step-by-step explanation:
Step 1: Write limit
[tex]\lim_{x \to -a} \frac{x^2-a^2}{x^4-a^4}[/tex]
Step 2: Factor
[tex]\lim_{x \to -a} \frac{(x+a)(x-a)}{(x+a)(x-a)(x^2+a^2)}[/tex]
Step 3: Simplify
[tex]\lim_{x \to -a} \frac{1}{x^2+a^2}[/tex]
Step 4: Substitute
[tex]\frac{1}{(-a)^2+a^2}[/tex]
Step 5: Evaluate
[tex]\frac{1}{a^2+a^2}[/tex]
Step 6: Simplify
[tex]\frac{1}{2a^2}[/tex]
