finding limits using properties of limits question 14, 11.2.87 hw score: 86.67%, 13 of 15 points save…

finding limits using properties of limits question 14, 11.2.87 hw score: 86.67%, 13 of 15 points save points: 0 of 1 horizontal asymptotes of graphs can be described using limits. if the graph of a function f has a horizontal asymptote y = l to the right, then it can be said that lim f(x)=l. this is called a limit at infinity. note that a limit at infinity describes the end - behavior of the graph to the right. a similar limit can be defined to describe the end - behavior to the left. use your knowledge of horizontal asymptotes and the graphs of rational, exponential, and logistic functions to find the limit at infinity. lim (7x²)/(x² + 3x + 2) x→+∞ select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. lim (7x²)/(x² + 3x + 2)= (type an integer or a simplified fraction.) x→+∞ b. the limit does not exist

finding limits using properties of limits question 14, 11.2.87 hw score: 86.67%, 13 of 15 points save points: 0 of 1 horizontal asymptotes of graphs can be described using limits. if the graph of a function f has a horizontal asymptote y = l to the right, then it can be said that lim f(x)=l. this is called a limit at infinity. note that a limit at infinity describes the end - behavior of the graph to the right. a similar limit can be defined to describe the end - behavior to the left. use your knowledge of horizontal asymptotes and the graphs of rational, exponential, and logistic functions to find the limit at infinity. lim (7x²)/(x² + 3x + 2) x→+∞ select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. lim (7x²)/(x² + 3x + 2)= (type an integer or a simplified fraction.) x→+∞ b. the limit does not exist

Answer

Explanation:

Step1: Divide numerator and denominator by highest - power of x

Divide both the numerator and denominator of $\frac{7x^{2}}{x^{2}+3x + 2}$ by $x^{2}$. We get $\lim_{x\rightarrow\infty}\frac{7x^{2}/x^{2}}{(x^{2}+3x + 2)/x^{2}}=\lim_{x\rightarrow\infty}\frac{7}{1+\frac{3}{x}+\frac{2}{x^{2}}}$.

Step2: Evaluate limits of individual terms

As $x\rightarrow\infty$, $\lim_{x\rightarrow\infty}\frac{3}{x}=0$ and $\lim_{x\rightarrow\infty}\frac{2}{x^{2}} = 0$. So, $\lim_{x\rightarrow\infty}\frac{7}{1+\frac{3}{x}+\frac{2}{x^{2}}}=\frac{7}{1 + 0+0}$.

Step3: Calculate the final limit

$\frac{7}{1+0 + 0}=7$.

Answer:

A. $\lim_{x\rightarrow\infty}\frac{7x^{2}}{x^{2}+3x + 2}=7$