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Question Number 98004 by Ar Brandon last updated on 11/Jun/20

$$\underset{\mathrm{n}\to \mathrm{\infty }}{\lim }[\sin \left(\mathrm{n}\right)+4^{\mathrm{n}}\times \frac{3}{{\mathrm{n}}^2}\times \frac{\mathrm{n}+1}{{\mathrm{n}}^2-4}]$$

Commented by bobhans last updated on 11/Jun/20

$$\underset{\mathrm{n}\to \mathrm{\infty }}{\lim }\frac{\sin \mathrm{n}}{\mathrm{n}}\times \underset{\mathrm{n}\to \mathrm{\infty }}{\lim }\frac{3.4^{\mathrm{n}}}{\mathrm{n}}\times \underset{\mathrm{n}\to \mathrm{\infty }}{\lim }\frac{\mathrm{n}+1}{{\mathrm{n}}^2-4}$$$$=0\times \mathrm{\infty }\times 0=0$$$$[\underset{\mathrm{n}\to \mathrm{\infty }}{\lim }\frac{3.4^{\mathrm{n}}}{\mathrm{n}}=3\times \underset{\mathrm{n}\to \mathrm{\infty }}{\lim }\frac{\ln \left(4\right).4^{\mathrm{n}}}{1}=\mathrm{\infty }]$$

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