Limit of a Logratithmic cum Algebraic Function?

Calculus Level 5

lim ⁡ x → 0 ln ⁡ ( 1 + x 2014 ) − ( ln ⁡ ( 1 + x ) ) 2014 x 2015 = ? \large \lim_{x\to0} \frac{ \ln(1+x^{2014}) - ( \ln(1+x))^{2014} } {x^{2015}} = \ ?


The answer is 1007.

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Satyajit Mohanty by Satyajit Mohanty , 24, India

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1 solution

Satyajit Mohanty
Jul 7, 2015

10 Helpful 0 Interesting 0 Brilliant 0 Confused

@Satyajit Mohanty L'Hopital isn't necessary......we can expand using Binomial Theorem and see that all terms tend to 0 except 1007....

Aaghaz Mahajan - 3 years, 3 months ago

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