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### NCERT - Log misses the bus!

While Log tables as tools for calculation may be facing their extinction due to the "fitter" electronic calculators, Log continues to be important as it seems be an ingredient of some laws of nature. Effort to find Log as a chapter in NCERT syllabi (9th, 10th, 11th & 12th) would go in vain. If one tries hard enough then one finds the mention of Logarithmic series in the appendix of class 11th Mathematics. One wonders if there in no Log in class 11th or earlier then how can there be Logarithmic series in appendix? After all shouldn't Log be taught first? A search of word Log does not show anywhere else in class 11th portion. But then shouldn't Log be there in class 11th (or earlier)? After all there are so many applications in quadratic expressions & equations that are based on Log, so many problems related to domain & range based on Log, concept of pH, Henderson's equation for buffer solutions, work done in an isothermal process by an ideal gas etc. All the topics mentioned above are in class 11th portion. Finally, one can find Log in class 12th syllabus inside, "Continuity & Differentiability" which is after, "Functions". To get a feel of functions, it is necessary that students get into graphing but if NCERT is to be followed then graphs of Log cannot be understood properly when graphs of most standard and special functions are discussed. A simple and widely used topic Log must be introduced in early class formally and not so late. In fact in the past it was introduced before class 11th and it makes sense as students are introduced to pH before class 11th level.

NCERT should include Log in earlier class in future but at the moment, teachers should consider it including in 11th portion if not earlier.

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