Chapter 4: Applications of Derivatives - Additional and Advanced Exercises - Page 246: 11

$a=1,b=0,c=1$

Based on the given conditions, (ii) gives $f(-1)=0$. Using it in the function, we have $\frac{a-1}{b-cx+2}=0$, which gives $a=1$. Use condition (iii), to find the asymptotes. Letting $x\to\pm\infty$, we have $\lim_{x\to\pm\infty}(\frac{1+a/x}{bx+c+2/x})$ and for this limit to be $y=1$, we need $b=0$ and $c=1$. Thus the answers are $a=1,b=0,c=1$