13. [-/0.83 Points] DETAILS MY NOTES SCALCET9 2.XP.6.008. Find the limit. (If the limit is infinite, enter ' \( \infty \) ' or ' \( -\infty \) ', as appropriate. If the limit does not otherwise exist, enter DNI \( \lim _{x \rightarrow \infty} \frac{x^{2}}{\sqrt{x^{4}+9}} \) ASK YOUR TEA Fin

Calculate the limit \( \lim_{x\rightarrow \infty} \frac{x^{2}}{\sqrt{x^{4}+9}} \). Evaluate the limit by following steps: - step0: Evaluate using transformations: \(\lim _{x\rightarrow +\infty}\left(\frac{x^{2}}{\sqrt{x^{4}+9}}\right)\) - step1: Rewrite the expression: \(\lim _{x\rightarrow +\infty}\left(\frac{x^{2}}{\sqrt{1+\frac{9}{x^{4}}}\times x^{2}}\right)\) - step2: Reduce the fraction: \(\lim _{x\rightarrow +\infty}\left(\frac{1}{\sqrt{1+\frac{9}{x^{4}}}}\right)\) - step3: Rewrite the expression: \(\frac{\lim _{x\rightarrow +\infty}\left(1\right)}{\lim _{x\rightarrow +\infty}\left(\sqrt{1+\frac{9}{x^{4}}}\right)}\) - step4: Calculate: \(\frac{1}{\lim _{x\rightarrow +\infty}\left(\sqrt{1+\frac{9}{x^{4}}}\right)}\) - step5: Calculate: \(\frac{1}{1}\) - step6: Divide the terms: \(1\) The limit of \( \frac{x^{2}}{\sqrt{x^{4}+9}} \) as \( x \) approaches infinity is 1.