question_answer

Let \[f(x)={{x}^{3}}-{{x}^{2}}-3x-1,\,\,g(x)=(x+1)\,a\] and \[h(x)=\frac{f(x)}{g(x)}\]where h is a rational function such that:

(i) it is continuous every where except when \[x=-1\,,\]

(ii) \[\underset{x\to \infty }{\mathop{\lim }}\,h(x)=\infty \] and

(iii) \[\underset{x\to \infty }{\mathop{\lim }}\,h(x)=\frac{1}{2}\].

The value of h(1) is____.

Answer:

-0.5