Mathematics - Limits Question with Solution | TestHub

Using $f(x)/x\to 1$, expand the numerator: $x(1+a\cos x)-b\sin x=x(1+a-b)+x^3(-a/2+b/6)+O\left(x^5\right)$. Finiteness forces $1+a-b=0$, and the limit condition gives $-a/2+b/6=1$. Hence $a=-5/2,b=-3/2$, and $b/a=3/5=0.60$.