Question

Let f(x) be a continuously differentiable function on the interval (0, ∞) such that f(1) = 2 and
$\lim\limits_{t→x}\frac{t^{10}f(x)-x^{10}f(t)}{t^9-x^9}=1$
for each x > 0. Then, for all x > 0, f(x) is equal to

• A. $\frac{31}{11x}-\frac{9}{11}x^{10}$
• B. $\frac{9}{11x}+\frac{13}{11}x^{10}$
• C. $\frac{-9}{11x}+\frac{31}{11}x^{10}$
• D. $\frac{13}{11x}+\frac{9}{11}x^{10}$

Answer 1

Answer: (B)

$\frac{9}{11x}+\frac{13}{11}x^{10}$

Answer 2

The correct option is (B):$\frac{9}{11x}+\frac{13}{11}x^{10}$.