what is the horizontal asymptote of the graph of $f(x)=\\frac{x^{2}+3}{2x^{2}-7x}$?\ngive your answer in the…

what is the horizontal asymptote of the graph of $f(x)=\\frac{x^{2}+3}{2x^{2}-7x}$?\ngive your answer in the form $y = a$.\nprovide your answer below:

what is the horizontal asymptote of the graph of $f(x)=\\frac{x^{2}+3}{2x^{2}-7x}$?\ngive your answer in the form $y = a$.\nprovide your answer below:

Answer

Explanation:

Step1: Divide numerator and denominator by (x^2)

$$ \begin{align*} f(x)&=\frac{\frac{x^{2}}{x^{2}}+\frac{3}{x^{2}}}{\frac{2x^{2}}{x^{2}}-\frac{7x}{x^{2}}}\ &=\frac{1 + \frac{3}{x^{2}}}{2-\frac{7}{x}} \end{align*} $$

Step2: Find the limit as (x\to\pm\infty)

As (x\to\pm\infty), (\frac{3}{x^{2}}\to0) and (\frac{7}{x}\to0) $$ \lim_{x\to\pm\infty}f(x)=\frac{1 + 0}{2-0}=\frac{1}{2} $$

Answer:

(y = \frac{1}{2})