Question

Let $f\left(x\right)$ be polynomial of degree $4$ with roots $1,2,3,4$ and leading coefficient $1$ and $g\left(x\right)$ be the polynomial of degree $4$ with roots $1,\frac{1}{2},\frac{1}{3}$ and $\frac{1}{4}$ with leading coefficient $1$. Find $\underset{x\to 1}{lim}\frac{f\left(x\right)}{g\left(x\right)}$

• A. $-34$
• B. $-24$
• C. $24$
• D. $34$

Answer 1

Answer: (B)

$-24$

$\frac{f\left(x\right)}{g\left(x\right)}=\underset{x\to 1}{lim}\frac{(x-1)(x-2)(x-3)(x-4)}{(x-1)(x-\frac{1}{2})(x-\frac{1}{3})(x-\frac{1}{4})}=\frac{(-1)(-2)(-3)}{\frac{1}{2}\times \frac{2}{3}\times \frac{3}{4}}=-24$