?Evaluate the limit and justify each step by indicating the appropriate properties of

Step 1 of 2

Consider the given function is,

\(\lim _{x \rightarrow \infty} \frac{2 x^{2}-7}{5 x^{2}+x-3}\)

Apply limit law 5.

Divide both the numerator and the denominator by the highest power of x of the denominator.

\(\begin{aligned} \lim _{x \rightarrow \infty} \frac{2 x^{2}-7}{5 x^{2}+x-3} & =\lim _{x \rightarrow \infty} \frac{\frac{2 x^{2}}{x^{2}}-\frac{7}{x^{2}}}{\frac{5 x^{2}}{x^{2}}+\frac{x}{x^{2}}-\frac{3}{x^{2}}} \\ & =\lim _{x \rightarrow \infty} \frac{2-\frac{7}{x^{2}}}{5+\frac{1}{x}-\frac{3}{x^{2}}} \end{aligned}\)