?Find the limit or show that it does not exist.\(\lim _{u \rightarrow-\infty}\)Equation

Step 1 of 2

The given function to find the limit is,

\(\lim _{u \rightarrow-\infty} \frac{\left(u^{2}+1\right)\left(2 u^{2}-1\right)}{\left(u^{2}+2\right)^{2}}\)

Solving the above we get,

\(\begin{aligned} \lim _{u \rightarrow \infty} \frac{\left(u^{2}+1\right)\left(2 u^{2}-1\right)}{\left(u^{2}+2\right)^{2}} & =\lim _{u \rightarrow \infty} \frac{\left(u^{2}+1\right)\left(2 u^{2}-1\right)}{u^{4}+2 u^{2}+4} \\ & =\lim _{u \rightarrow \infty} \frac{u^{2}\left(1+\frac{1}{u^{2}}\right) u^{2}\left(2-\frac{1}{u^{2}}\right)}{u^{4}\left(1+\frac{2}{u^{2}}+\frac{4}{u^{2}}\right)} \end{aligned}\)