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### Secret of Life: An Old Story

There was once an argument among the gods over where to hide the secret of life so that men and women would not find it. One god said: Bury it under a mountain; they will never look there. No, the others said, one day they will find ways to dig up mountains and will uncover it. Another said : Sink it in the depths of the ocean; it will be safe there. No the others objected, humans will one day find a way to plumb the ocean's depths and find it easily. Finally another god said: Put it inside them; men and women will never think of looking for it there. All the gods agreed, and so that is how the secret of life came to be hidden within us.

By: Anonymous.

### $f(x)=x^6+2x^4+x^3+2x+3 $$\mathop {\lim }\limits_{x \to 1} \frac{{{x^n}f(1) - f(x)}}{{x - 1}} = 44$$n=?$

Let $f(x)=x^6+2x^4+x^3+2x+3,x \in R$. Then the natural number n for which $\mathop {\lim }\limits_{x \to 1} \frac{{{x^n}f(1) - f(x)}}{{x - 1}} = 44$ is _ _ _ _ . Solution Since the limit has $\left[ {\frac{0}{0}} \right]$ form, L.H. Rule is applicable. Thus, $\mathop {\lim }\limits_{x \to 1} n{x^{n - 1}}f(1) - f'(x) = 44$ $\therefore nf(1) - f'(1) = 44$ $\therefore n.9 - ({6.1^5} + {8.1^3} + {3.1^2} + 2.1) = 44$ $\Rightarrow 9n - 19 = 44$ $\Rightarrow n=7$