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Due to unavoidable reason, Ctanujit Classes will be closed from 1st November to 30th November 2018.
Postal Package will be available from 1st December 2018.

Use Of Polynomials in Finding Limits-New Way to Learn Mathematics


Basic knowledge of Polynomials seems to be useful sometimes to solve the problems involving Limits.
Basic knowledge of Algebra(Polynomials):- 
If we are given that f'(x)=constant then the polynomial is of the form f(x)=ax+b .
If we are given that f''(x)=constant then the polynomial is of the form f(x)=ax²+bx+c .

Problem:- Let f(0)=1, Lt{f"(x)}=4, where x->∞ and f(x) f(1) . Let f(x) is a polynomial for all x in R. Find f(2) .
Sol:- Since f"(x)=4, then f(x)=2x²+bx+c .
So, here f(0)=1 implies c=1 .
Now, f(1)=3+b.
 Since  f(x) f(1), so f'(1)=0 implying 4+b=0. So, b=-4 .
Therefore, f(x)=2x²-4x+1
Hence f(2)=1 .