Limit problem

Calculus Level pending

What is lim ⁡ n → ∞ n s i n ( x / n ) \lim _{ n\rightarrow \infty }{ nsin(x/n) } ?

x/2 x x^2 1/x

Christian Zinck by Christian Zinck , 22, USA

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1 solution

Christian Zinck
Dec 9, 2014

By substituting u for x/n, the problem can be rearranged to read x ( lim ⁡ u → 0 s i n ( u ) / u ) x(\lim _{ u\rightarrow 0 }{ sin(u)/ } u) . This, of course, is equivalent to x * 1, therefore the expression is equal to x.

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