A calculus problem by Sourabh Jangid

Calculus Level 5

lim n f ( 5 ( 4 + 15 ) n ) g ( 10 ( 4 + 14 ) n ) \large \lim_{n\to\infty} \dfrac{f\left(5 (4 + \sqrt{15})^n \right)}{g\left(10 (4 + \sqrt{14})^n \right)}

Let f ( x ) f(x) and g ( x ) g(x) be two periodic functions with fundamental periods of 5 and 10 respectively. Given that lim x 0 f ( x ) x = lim x 0 g ( x ) x = k \displaystyle \lim_{x\to0} \dfrac{f(x)}x = \lim_{x\to0} \dfrac{g(x)}x = k for some positive constant k k . Find the value of the limit above for positive integer n n .


The answer is 0.

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1 solution

Rohith M.Athreya
Jan 10, 2017

it would be useful to analyse what the fractional parts of both the binomial expansions in numerator and denominator will be

u do this and the next steps will be done all by themselves :P

Can you write a solution that is helpful to those who cannot solve it? Else I'm inclined to delete this solution to encourage others to contribute a relevant answer- \box S T A F F \box STAFF

A Former Brilliant Member - 4 years, 3 months ago

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