Question

\(\frac{d}{dx} \left[ \lim_{x \to a} \frac{x^n + a^n}{x + a} \right] \)

• A. \( \frac{a^n}{a} \)
• B. \( \frac{2a^n}{a} \)
• C. 1
• D. 0

Hint:

When the limit simplifies to a constant value, its derivative is 0, as the derivative of any constant is 0.

Answer 1

The Correct Option is D

We are given the limit expression: \[ \lim_{x \to a} \frac{x^n + a^n}{x + a} \] Step 1: Evaluate the limit
This is a standard limit problem. As \( x \to a \), the expression simplifies to: \[ \frac{a^n + a^n}{a + a} = \frac{2a^n}{2a} = \frac{a^n}{a} \]
Step 2: Differentiate the result
Once we have simplified the expression, we can differentiate it. Since we are differentiating a constant function, the derivative is 0. Thus, the answer is 0.