Question

$\displaystyle\lim_{x\to- \infty} \left(\frac{6x^{2} -\cos3x }{x^{2} + 5} - \frac{5x^{2}+3}{\sqrt{x^{6}+2}}\right) = $

• A. 11
• B. 0
• C. -1
• D. 1

Answer 1

Answer: (A)

$ \displaystyle\lim _{x \rightarrow-\infty}\left(\frac{6 x^{2}-\cos 3 x}{x^{2}+5}-\frac{5 x^{3}+3}{\sqrt{x^{6}+2}}\right) $
$=\displaystyle\lim _{x \rightarrow-\infty}\left(\frac{6-\frac{\cos 3 x}{x^{2}}}{1+\frac{5}{x^{2}}}-\frac{5+\frac{3}{x^{3}}}{\left(\frac{|x|^{3}}{x^{3}}\right) \sqrt{1+\frac{2}{x^{6}}}}\right) $
$\left[\because \displaystyle\lim _{x \rightarrow-\infty} \frac{\cos 3 x}{x^{2}}=0 \, \text{and} \,\displaystyle\lim _{x \rightarrow-\infty} \frac{|x|^{3}}{x^{3}}=-1\right] $
$= 6+5=11 $