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
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