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IIT-JEE & AIEEE Qualified Students

Till now, you had a mission.  The mission was to crack IIT-JEE and/or AIEEE.  Now that you have been successful in attaining your goal, it is equally important to set your next goal after enjoying the fruits of you labour.
The way things are going in the modern world, it looks that doing post graduation and even doctorate would be a better thing to do after graduation.  The modern world would be a world of specialisation.  I think, it would be a good policy to set your goal on theses lines.  Once you set your next goal, draw a plan how you intend to attain it in the next four years.
One more thing!  no matter what you choose your goal as, do read the book, "Law of Success" by Napoleon Hill and keep it with you throughout your life.
Life is a journey that never ends, no matter how high or how far you have travelled.
All the best!

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$f(x)=x^6+2x^4+x^3+2x+3 $

$\mathop {\lim }\limits_{x \to 1} \frac{{{x^n}f(1) - f(x)}}{{x - 1}} = 44$


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$ $\Rightarrow n=7$