question\nfind all horizontal asymptotes of the following function.\n f(x)=\frac{5 x^{2}-42 x + 49}{10…

question\nfind all horizontal asymptotes of the following function.\n f(x)=\frac{5 x^{2}-42 x + 49}{10 x^{2}-14 x} \nanswer attempt 1 out of 2\none horizontal asymptote\nno horizontal asymptotes\none horizontal asymptote\ntwo horizontal asymptotes

question\nfind all horizontal asymptotes of the following function.\n f(x)=\frac{5 x^{2}-42 x + 49}{10 x^{2}-14 x} \nanswer attempt 1 out of 2\none horizontal asymptote\nno horizontal asymptotes\none horizontal asymptote\ntwo horizontal asymptotes

Answer

Explanation:

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

$$ \begin{align*} \lim_{x\rightarrow\pm\infty}f(x)&=\lim_{x\rightarrow\pm\infty}\frac{5x^{2}-42x + 49}{10x^{2}-14x}\ &=\lim_{x\rightarrow\pm\infty}\frac{5-\frac{42}{x}+\frac{49}{x^{2}}}{10-\frac{14}{x}} \end{align*} $$

Step2: Evaluate the limit

As (x\rightarrow\pm\infty), (\frac{1}{x}\rightarrow0) and (\frac{1}{x^{2}}\rightarrow0). So (\lim_{x\rightarrow\pm\infty}\frac{5-\frac{42}{x}+\frac{49}{x^{2}}}{10-\frac{14}{x}}=\frac{5 - 0+0}{10-0}=\frac{1}{2})

Answer:

One Horizontal Asymptote (y = \frac{1}{2})