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**disclaimer** Hello;

$\displaystyle \lim_{n\rightarrow\infty}\sqrt{n^{10}-2n^2+2}$

To me, it's $\displaystyle \infty$, as I think we can write:

$\displaystyle \lim_{n\rightarrow\infty}\sqrt{n^{10}-2n^2+2}=$$\displaystyle \lim_{n\rightarrow\infty}\sqrt{n^{10}\left(1-\frac{2}{n^8}+\frac{2}{n^{10}}\right)}=$$\displaystyle \lim_{n\rightarrow\infty}\left(n^5\sqrt{1-\frac{2}{n^8}+\frac{2}{n^{10}}}\right)=$$\displaystyle \infty\cdot1=\infty$

But the answer in my textbook is $\displaystyle 1$. Am I missing something here? :confused: Mr F says: No. But your book probably is ..... the print for the continuation of the expression that you're taking the limit of.

Help appreciated. :)