If , find the number of integral values of…

MATHEMATICS · Subjective · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

If lim⁡n→∞n⋅3nn⋅(x−1)n+n⋅3n+1−3n=13\displaystyle\lim_{n\to\infty}\frac{n\cdot3^n}{n\cdot(x-1)^n+n\cdot3^{n+1}-3^n}=\frac13, find the number of integral values of xx.

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