Question

If $f(a) = 2$, $f'(a) = 1$, $g(a) = -1$, $g'(a) = 2$, then as $x$ approaches $a$, $\frac{g(x)f(a)-g(a)f(x)}{(x-a)}$ approaches}

• A. 3
• B. 5
• C.
• D.

Hint:

Recognize expressions of the form $\lim_{x \to a} \frac{f(x)g(a) - f(a)g(x)}{x-a}$ as variations of the difference quotient. Applying L'Hopital's Rule (differentiating numerator and denominator) often simplifies such limits quickly. The result is typically $f'(a)g(a) - f(a)g'(a)$ or similar, depending on the exact form.

Answer 1

The Correct Option is A