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IITM looking for satellite campus

When the IIT were set-up, they might be located far away from the main city township. However, as the population has grown so has the contruction. If an IIT wants to expand now, it is likely to find various existing constructions in its vicinity. It can go for more constructions inside the campus, but it may only be possbile at the cost of greenery if existing constructions are not tampered with. Another option is to go for high rise constructions, but it will lead to increased population density which is also not desirable.

Hence, the concept of extended arm or satellite campus looks appropriate to IITM. However, such concepts need to be approved by the central govenment.

$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, $\mathop {\lim }\limits_{x \to 1} n{x^{n - 1}}f(1) - f'(x) = 44$ $\therefore nf(1) - f'(1) = 44$ $\therefore n.9 - ({6.1^5} + {8.1^3} + {3.1^2} + 2.1) = 44$ $\Rightarrow 9n - 19 = 44$ $\Rightarrow n=7$